{"id":25818,"date":"2019-03-07T15:55:24","date_gmt":"2019-03-07T10:25:24","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=25818"},"modified":"2020-01-31T16:02:34","modified_gmt":"2020-01-31T10:32:34","slug":"trigonometry-questions-for-ssc-chsl-exam-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/trigonometry-questions-for-ssc-chsl-exam-pdf\/","title":{"rendered":"Trigonometry Questions for SSC CHSL Exam PDF"},"content":{"rendered":"<h2><strong><span style=\"text-decoration: underline;\">Trigonometry Questions for SSC CHSL Exam PDF:<\/span><\/strong><\/h2>\n<p>SSC CHSL Trignometry Questions download PDF based on previous year question paper of SSC CHSL exam. 25 Very important Trignometry questions for SSC CHSL Exam.<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/downloads\/3547\" target=\"_blank\" class=\"btn btn-danger  download\">Download Trigonometry Questions for SSC CHSL Exam PDF<\/a><\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/ssc\/pricing\/ssc-unlimited\" target=\"_blank\" class=\"btn btn-info \">Get 200 SSC mocks for just Rs. 249. Enroll here<\/a><\/p>\n<p>Take a <a href=\"https:\/\/cracku.in\/ssc-chsl-mock-tests\" target=\"_blank\" rel=\"noopener\">free mock test for SSC CHSL<\/a><\/p>\n<p>Download <a href=\"https:\/\/cracku.in\/ssc-chsl-question-papers\" target=\"_blank\" rel=\"noopener\">SSC CHSL Previous Papers<\/a><\/p>\n<p>More <a href=\"https:\/\/cracku.in\/blog\/ssc-chsl-important-questions-and-answers-pdf\/\" target=\"_blank\" rel=\"noopener\">SSC CHSL Important Questions and Answers PDF<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><b>Question 1:\u00a0<\/b>If $\\sin x+\\frac{1}{\\sin x}=2$ then $\\cos ^5 x+\\cot ^{5} x=?$<\/p>\n<p>a)\u00a00<br \/>\nb)\u00a0-1<br \/>\nc)\u00a01<br \/>\nd)\u00a02<\/p>\n<p><b>Question 2:\u00a0<\/b>If $cos^2x + (1 + sinx)^2 = 3$, then find the value of cosec x + sin(60+x), where 0\u00ba &lt; x &lt; 90\u00ba?<\/p>\n<p>a)\u00a03<br \/>\nb)\u00a02<br \/>\nc)\u00a0$2\\frac{1}{2}$<br \/>\nd)\u00a0$3\\frac{1}{2}$<\/p>\n<p><b>Question 3:\u00a0<\/b>If $x$ and $y$ are acute angles such that their sum is less than $90^{\\circ}$ . If $\\cos(2x-20^{\\circ})=\\sin(2y+20^{\\circ})$ , then the value of $\\tan(x+y)$ is<\/p>\n<p>a)\u00a0$0$<br \/>\nb)\u00a0$1$<br \/>\nc)\u00a0$\\frac{1}{\\sqrt{3}}$<br \/>\nd)\u00a0$\\sqrt{3}$<\/p>\n<p><b>Question 4:\u00a0<\/b>If x is an acute angle such that<br \/>\nTan (4x &#8211; 50\u00b0) = Cot ( 50\u00b0 &#8211; x), then the value of x would be?<\/p>\n<p>a)\u00a060<br \/>\nb)\u00a045<br \/>\nc)\u00a050<br \/>\nd)\u00a030<\/p>\n<p><b>Question 5:\u00a0<\/b>If cosec 9x= sec 9x (0 &lt;x&lt;10), what is the value of x?<\/p>\n<p>a)\u00a09\u00b0<br \/>\nb)\u00a03\u00b0<br \/>\nc)\u00a05\u00b0<br \/>\nd)\u00a06\u00b0<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/ssc-chsl-question-papers\" target=\"_blank\" class=\"btn btn-primary \">SSC CHSL PREVIOUS PAPERS<\/a><\/p>\n<p><b>Question 6:\u00a0<\/b>If $\\sin x+1=\\frac{2}{\\sin x} $ then $\\cos ^3 x+ \\mathrm{cosec} ^{-3} x=?$<\/p>\n<p>a)\u00a00<br \/>\nb)\u00a0-1<br \/>\nc)\u00a01<br \/>\nd)\u00a02<\/p>\n<p><b>Question 7:\u00a0<\/b>If $\\frac{sin2x}{sinx} + cos2x + sin^2x = 0$, find the value of x, if $0 \\leq x \\leq 180$.<\/p>\n<p>a)\u00a045\u00ba<br \/>\nb)\u00a090\u00ba<br \/>\nc)\u00a0180\u00ba<br \/>\nd)\u00a0More than one value is possible<\/p>\n<p><b>Question 8:\u00a0<\/b>If $\\frac{sin^2 \\Theta}{4} = \\frac{cos^2 \\Theta}{9}$. Find the value of $tan^2 \\Theta &#8211; cot^2 \\Theta$.<\/p>\n<p>a)\u00a01\/6<br \/>\nb)\u00a013\/27<br \/>\nc)\u00a01\/18<br \/>\nd)\u00a0None of these<\/p>\n<p><b>Question 9:\u00a0<\/b>If $\\sec^4 x-\\tan^4 x=4+4sin^2 x$ then $ x=?$ (0&lt;x&lt;90\u00b0)<\/p>\n<p>a)\u00a045\u00b0<br \/>\nb)\u00a030\u00b0<br \/>\nc)\u00a075\u00b0<br \/>\nd)\u00a060\u00b0<\/p>\n<p><b>Question 10:\u00a0<\/b>Simplify the expression $\\sqrt{\\frac{1+cosx}{1-cosx}}$.<\/p>\n<p>a)\u00a0sec x + tan x<br \/>\nb)\u00a0sin x<br \/>\nc)\u00a0cosec x + cot x<br \/>\nd)\u00a0cos x<\/p>\n<p>&nbsp;<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/ssc-chsl-mock-tests\" target=\"_blank\" class=\"btn btn-danger \">SSC CHSL FREE MOCK TEST<\/a><\/p>\n<p><b>Question 11:\u00a0<\/b>If $sinx = 1 &#8211; cos x$, find the value of cos 2x.<\/p>\n<p>a)\u00a00<br \/>\nb)\u00a01<br \/>\nc)\u00a0$\\frac{1}{2}$<br \/>\nd)\u00a0$\\frac{\\sqrt{3}}{2}$<\/p>\n<p><b>Question 12:\u00a0<\/b>If it is known that<br \/>\n$\\tan\\theta + \\cot\\theta = 2$, then find the value of $\\tan^3\\theta + \\cot^3\\theta$<\/p>\n<p>a)\u00a0$\\sqrt{5}$<br \/>\nb)\u00a02<br \/>\nc)\u00a0$1 + \\sqrt{3}$<br \/>\nd)\u00a0$2 + \\sqrt{3}$<\/p>\n<p><b>Question 13:\u00a0<\/b>If $\\sin x+\\frac{1}{\\sin x}=\\frac{5}{2}$ then $\\tan {x}+\\cot {x}=?$<\/p>\n<p>a)\u00a00<br \/>\nb)\u00a0$\\frac{2}{\\sqrt3}$<br \/>\nc)\u00a0$\\frac{4}{\\sqrt3}$<br \/>\nd)\u00a0$\\frac{\\sqrt3}{2}$<\/p>\n<p><b>Question 14:\u00a0<\/b>If $\\cos x+\\frac{1}{\\cos x}=2$ then $\\sin ^{5} x+\\sec ^{-5} x=?$<\/p>\n<p>a)\u00a0-1<br \/>\nb)\u00a00<br \/>\nc)\u00a01<br \/>\nd)\u00a02<\/p>\n<p><b>Question 15:\u00a0<\/b>If $\\tan x+\\frac{1}{\\tan x}=2$ then $\\sin ^{5} x+\\cos ^{5} x=?$<\/p>\n<p>a)\u00a0$\\frac{1}{4\\sqrt{2}}$<br \/>\nb)\u00a0$\\frac{1}{2\\sqrt{2}}$<br \/>\nc)\u00a0$\\frac{1}{\\sqrt{2}}$<br \/>\nd)\u00a0$\\frac{1}{8\\sqrt{2}}$<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/ssc-study-material\" target=\"_blank\" class=\"btn btn-primary \">FREE SSC MATERIAL &#8211; 18000 FREE QUESTIONS<\/a><\/p>\n<p><b>Question 16:\u00a0<\/b>The maximum value of sin \u03b8 + cos \u03b8 is<\/p>\n<p>a)\u00a0$1$<br \/>\nb)\u00a0$\\sqrt{2}$<br \/>\nc)\u00a0$2$<br \/>\nd)\u00a0$3$<\/p>\n<p><b>Question 17:\u00a0<\/b>If $sin \\Theta + cosec \\Theta = 5$, Find the value of $sin^3 \\Theta + cosec ^3 \\Theta $.<\/p>\n<p>a)\u00a096<br \/>\nb)\u00a0115<br \/>\nc)\u00a0110<br \/>\nd)\u00a0None of these<\/p>\n<p><b>Question 18:\u00a0<\/b>The value of $cos^2 30^{\\circ} + sin^2 60^{\\circ} + tan^2 45^{\\circ} + sec^2 60^{\\circ} + cos0^{\\circ}$ is<\/p>\n<p>a)\u00a0$4\\frac{1}{2}$<br \/>\nb)\u00a0$5\\frac{1}{2}$<br \/>\nc)\u00a0$6\\frac{1}{2}$<br \/>\nd)\u00a0$7\\frac{1}{2}$<\/p>\n<p><b>Question 19:\u00a0<\/b>If $cos x + cos^{2} x = 1,$ then $sin^{8} x + 2 sin^{6} x + sin^{4}$ x is equal to<\/p>\n<p>a)\u00a00<br \/>\nb)\u00a03<br \/>\nc)\u00a02<br \/>\nd)\u00a01<\/p>\n<p><b>Question 20:\u00a0<\/b>If $x= p$ $cosec \u03b8$ and $y= q$ $cot \u03b8$, then the value of $\\frac{x^2}{p^2}-\\frac{y^2}{q^2}$ is<\/p>\n<p>a)\u00a0$sin^{2} \u03b8$<br \/>\nb)\u00a0$tan\u03b8$<br \/>\nc)\u00a0$1$<br \/>\nd)\u00a0$0$<\/p>\n<p>&nbsp;<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.cracku.app\" target=\"_blank\" class=\"btn btn-info \">DOWNLOAD APP TO ACESSES DIRECTLY ON MOBILE<\/a><\/p>\n<p><b>Question 21:\u00a0<\/b>Find the value of tan 4\u00b0 tan 43\u00b0 tan 47 tan 86\u00b0<\/p>\n<p>a)\u00a0$\\frac{2}{3}$<br \/>\nb)\u00a0$1$<br \/>\nc)\u00a0$\\frac{1}{2}$<br \/>\nd)\u00a0$2$<\/p>\n<p><b>Question 22:\u00a0<\/b>If $x cos\u03b8 &#8211; sin\u03b8 = 1,$ then $x^{2} &#8211; (1 +x^{2}) sin\u03b8$ equals<\/p>\n<p>a)\u00a02<br \/>\nb)\u00a01<br \/>\nc)\u00a0&#8211; 1<br \/>\nd)\u00a00<\/p>\n<p><b>Question 23:\u00a0<\/b>If $sin \u03b8 + sin^{2} \u03b8 = 1$ then $cos^2 \u03b8 + cos^4 \u03b8$ is equal to<\/p>\n<p>a)\u00a0None<br \/>\nb)\u00a01<br \/>\nc)\u00a0$Sin \u03b8 \/cos^{2} \u03b8$<br \/>\nd)\u00a0$cos^{2}\u03b8 \/ Sin \u03b8$<\/p>\n<p><b>Question 24:\u00a0<\/b>The value of tan1\u00b0tan2\u00b0tan3\u00b0 \u2026\u2026\u2026\u2026\u2026tan89\u00b0 is<\/p>\n<p>a)\u00a01<br \/>\nb)\u00a0-1<br \/>\nc)\u00a00<br \/>\nd)\u00a0None of the options<\/p>\n<p><b>Question 25:\u00a0<\/b>If 0\u00b0 \u2264 A \u2264 90\u00b0, the simplified form of the given expression sin A cos A (tan A &#8211; cot A) is<\/p>\n<p>a)\u00a01<br \/>\nb)\u00a01 &#8211; 2 $sin^2$ A<br \/>\nc)\u00a02 $sin^2$ A &#8211; 1<br \/>\nd)\u00a01 &#8211; cos A<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/ssc-stenographer-mock-test\" target=\"_blank\" class=\"btn btn-primary \">FREE MOCK TEST FOR SSC STENOGRAPHER<\/a><\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Answers &amp; Solutions:<\/strong><\/span><\/p>\n<p><strong>1)\u00a0Answer\u00a0(A)<\/strong><\/p>\n<p>$\\sin x+\\frac{1}{\\sin x}=2$<br \/>\n=&gt;$\\sin^2 x+1=2\\sin x$<br \/>\n=&gt;$(\\sin x-1)^2=0$<br \/>\n=&gt;$\\sin x = 1$<br \/>\n=&gt;$\\cos x = 0$<br \/>\nThe given expression would be,<br \/>\n$\\cos ^5 x+\\cot ^{5} x$<br \/>\n$\\cos ^5 x+\\frac{\\cos^5 x}{\\sin^5 x}$<br \/>\n$=0$<\/p>\n<p><strong>2)\u00a0Answer\u00a0(A)<\/strong><\/p>\n<p>$cos^2x + (1 + sinx)^2 = 3$<br \/>\n=&gt; $cos^2x + 1 + sin^2x + 2sinx = 3$ (Since $ cos^2x + sin^2x = 1$)<br \/>\n=&gt; $2 sin x = 1$ or sin x = \u00bd which means x=30 degrees [Solution in the first quadrant]<br \/>\n=&gt; cosec x = 1\/sin x = 2 and sin (60+x) = sin 90 = 1<br \/>\n=&gt; The value of the expression is 2+1 = 3<\/p>\n<p><strong>3)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>Given that , $x+y&lt;90^{\\circ} \\dots (1)$<br \/>\n$\\implies\\cos(2x-20^{\\circ})=\\cos(90^{\\circ}-(2y+20^{\\circ}))$<br \/>\nUsing the given property in $(1)$<br \/>\n$\\implies 2x-20^{\\circ}=70^{\\circ}-2y$<br \/>\n$\\implies 2x+2y=90^{\\circ}$<br \/>\n$\\implies x+y=45^{\\circ}$<br \/>\n$\\implies \\tan(x+y)=1 $<br \/>\nHence , the correct option is B<\/p>\n<p><strong>4)\u00a0Answer\u00a0(D)<\/strong><\/p>\n<p>We know that Tan ( 90 &#8211; x) = Cot x and Cot (90 &#8211; x) = Tanx<br \/>\nSo 4x &#8211; 50 = 90 &#8211; y<br \/>\nThen 50 &#8211; x will be y<br \/>\n=&gt; y = 50 &#8211; x<br \/>\nx + y = 50<br \/>\nMoreover,<br \/>\n90 &#8211; y = 4x &#8211; 50<br \/>\n=&gt; 4x + y = 140<br \/>\nSubtracting the two equations, we get<br \/>\n3x = 90<br \/>\n=&gt; x = 30<br \/>\nHence the correct answer is option D.<\/p>\n<p><strong>5)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>If cosec 9x= sec 9x,<br \/>\nThen $\\sin 9x=\\cos 9x$<br \/>\nIn the first quadrant cos and sin are equal when $9x =45$\u00b0<br \/>\nHence, x = 5\u00b0<\/p>\n<p><strong>6)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>$\\sin x+1=\\frac{2}{\\sin x} $<br \/>\n=&gt;$\\sin^2 x+\\sin x=2$<br \/>\n=&gt;$(\\sin x-1)(\\sin x+2)=0$<br \/>\nAs $\\sin x$ can only take values between -1 and 1,<br \/>\n=&gt;$\\sin x = 1$<br \/>\n=&gt;$\\cos x = 0$<br \/>\nThe given expression would be,<br \/>\n$\\cos ^3 x+ \\mathrm{cosec}^{-3} x$<br \/>\n$\\cos ^3 x + \\sin^3 x$<br \/>\n$=1$<\/p>\n<p><strong>7)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>$\\frac{sin2x}{sinx} + cos2x + sin^2x = 0$<br \/>\nWe know that $sin2x = 2 sinx cosx$ and $cos2x=cos^2x-sin^2x$<br \/>\n=&gt; $2cosx + cos^2x = 0$<br \/>\n=&gt; cos x =0 or cos x =2<br \/>\nNow, cos x =2 is not possible.<br \/>\n=&gt; cos x = 0<br \/>\nIn the range, $0 \\leq x \\leq 180$, cos x =0 at only 90\u00ba<br \/>\nThus, B is the correct answer.<\/p>\n<p><strong>8)\u00a0Answer\u00a0(D)<\/strong><\/p>\n<p>$\\frac{sin^2 \\Theta}{4} = \\frac{cos^2 \\Theta}{9}$<br \/>\n==&gt; $\\frac{sin^2 \\Theta}{cos^2 \\Theta}$ = $\\frac{4}{9}$<br \/>\n==&gt; $tan^2 \\Theta = \\frac{4}{9}$<br \/>\n==&gt; $cot^2 \\Theta = \\frac{9}{4}$<br \/>\n==&gt; $tan^2 \\Theta &#8211; cot^2 \\Theta$ = 4\/9 &#8211; 9\/4 = -65\/36<br \/>\nSince there is no such option, the correct option to choose is D.<\/p>\n<p><strong>9)\u00a0Answer\u00a0(D)<\/strong><\/p>\n<p>$\\sec^4 x-\\tan^4 x=4+4sin^2 x$<br \/>\n$(sec^2 x-\\tan^2 x)( sec^2 x+\\tan^2 x)=4+4sin^2 x$<br \/>\n$(1)( sec^2 x+\\tan^2 x)=4+4sin^2 x$ (as $sec^2 x-\\tan^2 x = 1$)<br \/>\n$\\frac{(1+ sin^2 x)}{cos^2 x} = 4(1+sin^2 x) $<br \/>\n$cos^2 x = \\frac{1}{4}$<br \/>\n$ cos x = \\frac{1}{2} or \\frac{-1}{2}$<br \/>\nHere, $cosx$ cannot be negative as (0&lt;x&lt;90\u00b0)<\/p>\n<p>Hence, $ cos x = \\frac{1}{2}$ and $ x = 60$\u00b0<\/p>\n<p><strong>10)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>$\\sqrt{\\frac{1+cosx}{1-cosx}}$<br \/>\nMultiplying the numerator and denominator by 1+cosx, we get<br \/>\n$\\sqrt{\\frac{(1+cosx)^2}{(1-cosx)(1+cosx)}}$<br \/>\n=&gt; $\\sqrt{\\frac{(1+cosx)^2}{(1- cos^2x}}$<br \/>\n=&gt; $\\frac{1+cosx}{sinx}$ = cosecx + cotx$<\/p>\n<p>&nbsp;<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/blog\/general-knowledge-questions-and-answers-for-competitive-exams-pdf\/\" target=\"_blank\" class=\"btn btn-danger \">GK Questions And Answers PDF<\/a><\/p>\n<p><strong>11)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>$sinx = 1 &#8211; cos x$<br \/>\n=&gt; $sinx + cos x = 1 $<br \/>\nSquaring both sides we get,<br \/>\n$sin^2x + cos^2x + 2 sinx cos x = 1$<br \/>\n=&gt; $1 + sin2x = 1$<br \/>\n=&gt; sin 2x = 0 or x=0<br \/>\n=&gt; cos 2x = 1<\/p>\n<p><strong>12)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>$\\tan\\theta + \\cot\\theta = 2$<br \/>\nCubing both sides we get<br \/>\n$\\tan^3\\theta + \\cot^3\\theta + 3\\tan\\theta*\\cot\\theta(\\tan\\theta+\\cot\\theta) = 8$<br \/>\n=&gt; $\\tan^3\\theta + \\cot^3\\theta + 3*2 = 8$<span class=\"redactor-invisible-space\"><br \/>\n=&gt; $\\tan^3\\theta + \\cot^3\\theta = 2$<span class=\"redactor-invisible-space\"><br \/>\n<\/span><br \/>\n<\/span><\/p>\n<p><strong>13)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>$\\sin x+\\frac{1}{\\sin x}=\\frac{5}{2}$<br \/>\n=&gt;$2\\sin^2 x-5\\sin x+2=0$<br \/>\n=&gt;$(\\sin x-1\/2)(\\sin x-2)=0$<br \/>\n=&gt;$\\sin x = 1\/2$<br \/>\n=&gt;$x=30$ degrees<br \/>\n=&gt;$\\tan x = \\frac{1}{\\sqrt3}$<br \/>\n=&gt;$\\cot x = \\sqrt3$<br \/>\nThe given expression would be,<br \/>\n$\\tan {x}+\\cot {x}$<br \/>\n$=\\frac{1}{\\sqrt3}+\\sqrt3$<br \/>\n$=\\frac{4}{\\sqrt3}$<\/p>\n<p><strong>14)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>$\\cos x+\\frac{1}{\\cos x}=2$<br \/>\n=&gt;$\\cos^2 x+1=2\\cos x$<br \/>\n=&gt;$(\\cos x-1)^2=0$<br \/>\n=&gt;$\\cos x = 1$<br \/>\n=&gt;$\\sin x = 0$<br \/>\nThe given expression is,<br \/>\n$\\sin ^5 x+\\sec ^{-5} x$<br \/>\n$= \\sin ^5 x+\\frac{1}{\\cos^5 x}$<br \/>\n$=0+1 = 1$<\/p>\n<p><strong>15)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>$\\tan x+\\frac{1}{\\tan x}=2$<br \/>\n=&gt;$\\tan^2 x+1=2\\tan x$<br \/>\n=&gt;$(\\tan x-1)^2=0$<br \/>\n=&gt;$\\tan x = 1$<br \/>\n=&gt;$\\sin x = \\frac{1}{\\sqrt{2}}$<br \/>\n=&gt;$\\cos x = \\frac{1}{\\sqrt{2}}$<br \/>\nThe given expression would be,<br \/>\n$ \\sin ^5 x+\\cos ^{5} x$<br \/>\n$ \\sin ^5 x+\\cos^5 {x}$<br \/>\n$=\\frac{1}{4\\sqrt{2}}+\\frac{1}{4\\sqrt{2}} = \\frac{1}{2\\sqrt{2}}$<\/p>\n<p><strong>16)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>for asin \u03b8 + bcos \u03b8 + c,<br \/>\nmaximum value = $c+\\sqrt{a^{2}+b^{2}}$<br \/>\nminimum value = $c-\\sqrt{a^{2}+b^{2}}$<br \/>\nfor sin \u03b8 + cos \u03b8 , a = 1, b = 1, c = 0<br \/>\nmaximum value = $c+\\sqrt{a^{2}+b^{2}}=0+\\sqrt{1^{2}+1^{2}}=\\sqrt{2}$<br \/>\nso the answer is option B.<\/p>\n<p><strong>17)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>$sin \\Theta + cosec \\Theta = 5$<br \/>\n==&gt; $(sin \\Theta + cosec \\Theta)^3 = 5^3$<br \/>\n==&gt;$ sin^3 \\Theta + cosec ^3 \\Theta + 3*sin \\Theta * cosec \\Theta (sin \\Theta + cosec \\Theta)$ = 125<br \/>\n==&gt; $sin^3 \\Theta + cosec ^3 \\Theta + 3*5 = 125$<br \/>\n==&gt; $sin^3 \\Theta + cosec ^3 \\Theta $ = 110.<\/p>\n<p><strong>18)\u00a0Answer\u00a0(D)<\/strong><\/p>\n<p>Substituting values of angles, we get,<br \/>\n3\/4 + 3\/4+ 1 + 4 + 1 = 7.5. Option D is the right answer.<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/ssc-study-material\" target=\"_blank\" class=\"btn btn-info \">FREE SSC STUDY MATERIAL<\/a><\/p>\n<p><strong>19)\u00a0Answer\u00a0(D)<\/strong><\/p>\n<p>$cos x + cos^2 x = 1$<br \/>\n=&gt; $cos x = 1 &#8211; cos^2 x$<br \/>\n=&gt; $cos x = sin^2 x$<br \/>\n$\\therefore$ $sin^{8} x + 2 sin^{6} x + sin^{4} x$<br \/>\n<span class=\"redactor-invisible-space\">= $(sin^4 x + sin^2 x)^2$<br \/>\n<\/span><span class=\"redactor-invisible-space\">= $((cos x)^2 + sin^2 x)^2$<br \/>\n<\/span><span class=\"redactor-invisible-space\">= $(cos^2 x + sin^2 x)^2 = 1$<\/span><\/p>\n<p><strong>20)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>$x= p$ $cosec \u03b8$<br \/>\n=&gt; $cosec\\theta$ = $\\frac{x}{p}$<br \/>\nAlso, $y= q$ $cot \u03b8$<br \/>\n<span class=\"redactor-invisible-space\">=&gt; $cot\\theta$ = $\\frac{y}{q}$<br \/>\n<\/span><span class=\"redactor-invisible-space\">$\\because$ $cosec^2\\theta-cot^2\\theta$ = 1<br \/>\n<\/span><span class=\"redactor-invisible-space\">=&gt; $\\frac{x^2}{p^2}$ &#8211; $\\frac{y^2}{q^2}$ = 1<\/span><\/p>\n<p><strong>21)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>Expression : tan 4\u00b0 tan 43\u00b0 tan 47 tan 86\u00b0<br \/>\n$\\because$ $tan(90-\\theta) = cot\\theta$<br \/>\n=&gt; $tan 4^{\\circ} = tan(90^{\\circ}-86^{\\circ}) = cot 86^{\\circ}$<br \/>\nSimilarly, $tan 43^{\\circ} = cot 47^{\\circ}$<br \/>\n=&gt; $(cot 86^{\\circ} \\times tan 86^{\\circ}) * (tan 47^{\\circ} \\times cot 47^{\\circ})$<br \/>\nUsing, $tan\\theta cot\\theta$ = 1<br \/>\n=&gt; 1*1 = 1<\/p>\n<p><strong>22)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>Expression : $x cos\u03b8 &#8211; sin\u03b8 = 1$<br \/>\n=&gt; $x = \\frac{1}{cos\\theta} + \\frac{sin\\theta}{cos\\theta}$<br \/>\n=&gt; $x = sec\\theta + tan\\theta$ &#8212;&#8212;&#8212;&#8212;&#8211;Eqn(1)<br \/>\n$\\because$ $sec^2\\theta &#8211; tan^2\\theta = 1$<br \/>\n=&gt; $(sec\\theta + tan\\theta)(sec\\theta &#8211; tan\\theta) = 1$<br \/>\n=&gt; $(sec\\theta &#8211; tan\\theta) = \\frac{1}{x}$ &#8212;&#8212;&#8212;&#8212;&#8211;Eqn(2)<br \/>\nAdding eqns(1)&amp;(2)<br \/>\n=&gt; $2sec\\theta = x + \\frac{1}{x} = \\frac{x^2 + 1}{x}$<br \/>\n=&gt; $sec\\theta = \\frac{x^2 + 1}{2x}$<br \/>\nSubtracting eqn(2) from (1)<br \/>\n=&gt; $2tan\\theta = x &#8211; \\frac{1}{x} = \\frac{x^2 &#8211; 1}{x}$<br \/>\n=&gt; $tan\\theta = \\frac{x^2 &#8211; 1}{2x}$<br \/>\nWe know that, $sin\\theta = \\frac{tan\\theta}{sec\\theta}$<br \/>\n=&gt; $sin\\theta = \\frac{x^2 &#8211; 1}{2x} * \\frac{2x}{x^2 + 1}<br \/>\n=&gt; $sin\\theta = \\frac{x^2 &#8211; 1}{x^2 + 1}$<br \/>\nTo find : $x^2 &#8211; (1 + x^2) sin\u03b8 $<br \/>\n= $x^2 &#8211; (1 + x^2) * \\frac{x^2 &#8211; 1}{x^2 + 1}$<br \/>\n= $x^2 &#8211; (x^2 &#8211; 1)$<br \/>\n= 1<\/p>\n<p><strong>23)\u00a0Answer\u00a0(B)<\/strong><\/p>\n<p>Expression : $sin\\theta + sin^2\\theta = 1$<br \/>\n=&gt; $sin\\theta = 1 &#8211; sin^2\\theta$<br \/>\n=&gt; $sin\\theta = cos^2\\theta$<br \/>\nTo find : $cos^2\\theta + cos^4\\theta$<br \/>\n= $cos^2\\theta + (cos^2\\theta)^2$<br \/>\n= $cos^2\\theta + sin^2\\theta$<br \/>\n= 1<\/p>\n<p><strong>24)\u00a0Answer\u00a0(A)<\/strong><\/p>\n<p>Expression : tan1\u00b0tan2\u00b0tan3\u00b0 \u2026\u2026\u2026\u2026\u2026tan88\u00b0tan89\u00b0<br \/>\n$\\because$ $tan(90^{\\circ}-\\theta) = cot\\theta$<br \/>\n=&gt; tan 89\u00b0 = tan(90\u00b0-1) = cot 1\u00b0<br \/>\nSimilarly, tan 88\u00b0 = cot 2\u00b0 and so on till tan 46\u00b0 = cot 44\u00b0<br \/>\n=&gt; (tan1\u00b0tan2\u00b0tan3\u00b0&#8230;&#8230;.tan45\u00b0&#8230;&#8230;cot3\u00b0cot2\u00b0cot1\u00b0)<br \/>\nUsing, $tan\\theta cot\\theta$ = 1 and $tan45^{\\circ}$ = 1<br \/>\n=&gt; 1*1 = 1<\/p>\n<p><strong>25)\u00a0Answer\u00a0(C)<\/strong><\/p>\n<p>Expression : $sin A cos A (tan A &#8211; cot A)$<br \/>\n= $sin A cos A (\\frac{sin A}{cos A} &#8211; \\frac{cos A}{sin A})$<br \/>\n= $sin A cos A (\\frac{sin^2 A &#8211; cos^2 A}{sin A cos A})$<br \/>\n= $sin^2 A &#8211; cos^2 A$<br \/>\n= $sin^2 A &#8211; (1 &#8211; sin^2 A)$<br \/>\n= $2sin^2 A &#8211; 1$<\/p>\n<p>&nbsp;<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/ssc-chsl-mock-tests\" target=\"_blank\" class=\"btn btn-primary \">FREE SSC CHSL MOCK TEST SERIES<\/a><\/p>\n<p>We hope this SSC CHSL Trignometry Questions will be highly useful for your preparation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trigonometry Questions for SSC CHSL Exam PDF: SSC CHSL Trignometry Questions download PDF based on previous year question paper of SSC CHSL exam. 25 Very important Trignometry questions for SSC CHSL Exam. Take a free mock test for SSC CHSL Download SSC CHSL Previous Papers More SSC CHSL Important Questions and Answers PDF &nbsp; Question [&hellip;]<\/p>\n","protected":false},"author":21,"featured_media":25823,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[169,125,378],"tags":[],"class_list":{"0":"post-25818","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-downloads","8":"category-featured","9":"category-ssc-chsl"},"better_featured_image":{"id":25823,"alt_text":"Trigonometry Questions for SSC CHSL Exam PDF","caption":"Trigonometry Questions for SSC CHSL Exam PDF","description":"Trigonometry Questions for SSC CHSL Exam 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