{"id":40538,"date":"2020-02-14T18:04:06","date_gmt":"2020-02-14T12:34:06","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=40538"},"modified":"2020-02-14T18:04:09","modified_gmt":"2020-02-14T12:34:09","slug":"ssc-questions-on-trigonometry-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/ssc-questions-on-trigonometry-pdf\/","title":{"rendered":"SSC Questions on Trigonometry PDF"},"content":{"rendered":"

SSC Questions on Trigonometry PDF<\/strong><\/span><\/h1>\n

Download SSC Trigonometry Questions with answers PDF based on previous papers very useful for SSC  exams. Top-10 Very Important Questions for SSC Exams.<\/p>\n

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Download SSC Questions on Trigonometry PDF<\/a><\/p>\n

Question 1: <\/b>$5tan\\theta = 4$, then the value of $(\\frac{5sin\\theta – 3cos\\theta}{5sin\\theta + 3cos\\theta})$ is<\/p>\n

a) $\\frac{1}{7}$<\/p>\n

b) $\\frac{2}{7}$<\/p>\n

c) $\\frac{5}{7}$<\/p>\n

d) $\\frac{2}{5}$<\/p>\n

Question 2: <\/b>The least value of $(4sec^2\\theta + 9cosec^2\\theta)$ is<\/p>\n

a) 1<\/p>\n

b) 19<\/p>\n

c) 25<\/p>\n

d) 7<\/p>\n

Question 3: <\/b>If $x=cosec\\theta-sin\\theta$ and $y=sec\\theta-cos\\theta$, then the value of $x2<\/sup>y2<\/sup>(x2<\/sup> + y2<\/sup> + 3)$<\/p>\n

a) 0<\/p>\n

b) 1<\/p>\n

c) 2<\/p>\n

d) 3<\/p>\n

Question 4: <\/b>If $ 0 \\leq \\theta \\leq \\frac{\\pi}{2}$, $2ycos\\theta=sin\\theta$ and $\\frac{x}{2cosec\\theta}=y$, then the value of $x^2-4y^2$ is<\/p>\n

a) 1<\/p>\n

b) 2<\/p>\n

c) 3<\/p>\n

d) 4<\/p>\n

Question 5: <\/b>If $sin\\theta + \\sin^2\\theta = 1$, then the value of cos12<\/sup>$\\theta$ + 3cos10<\/sup>$\\theta$ + cos6<\/sup>$\\theta$ +  3cos8<\/sup>$\\theta$  – 1 is<\/p>\n

a) 0<\/p>\n

b) 1<\/p>\n

c) -1<\/p>\n

d) 2<\/p>\n

Question 6: <\/b>The value of $\\frac{1}{cosec\\theta – cot\\theta} – \\frac{1}{sin\\theta}$<\/p>\n

a) $cot\\theta$<\/p>\n

b) $cosec\\theta$<\/p>\n

c) $tan\\theta$<\/p>\n

d) $1$<\/p>\n

Question 7: <\/b>If $\\cos\\theta + \\sin\\theta = \\sqrt{2}\\cos\\theta$, then $\\cos\\theta – \\sin\\theta$ is<\/p>\n

a) -$\\sqrt{2}\\cos\\theta$<\/p>\n

b) -$\\sqrt{2}\\sin\\theta$<\/p>\n

c) $\\sqrt{2}\\sin\\theta$<\/p>\n

d) $\\sqrt{2}\\tan\\theta$<\/p>\n

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Question 8: <\/b>If $cos^4\\theta-sin^4\\theta=\\frac{2}{3}$, then the value of $1-2sin^2\\theta$ is,<\/p>\n

a) 0<\/p>\n

b) $\\frac{2}{3}$<\/p>\n

c) $\\frac{1}{3}$<\/p>\n

d) $\\frac{4}{3}$<\/p>\n

Question 9: <\/b>If $tan\\theta$ = 3\/4 and $\\theta$ is acute, then $cosec\\theta$ is equal to<\/p>\n

a) $\\frac{5}{3}$<\/p>\n

b) $2$<\/p>\n

c) $\\frac{1}{2}$<\/p>\n

d) $4$<\/p>\n

Question 10: <\/b>The value of $\\frac{1}{1 + tan^2\\theta}$ + $\\frac{1}{1 + cot^2\\theta}$ is<\/p>\n

a) 1<\/p>\n

b) 2<\/p>\n

c) $\\frac{1}{2}$<\/p>\n

d) $\\frac{1}{4}$<\/p>\n

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Answers & Solutions:<\/strong><\/span><\/p>\n

1) Answer (A)<\/strong><\/p>\n

Taking $cos\\theta$ outside in numerator and in denominator and making $tan\\theta$
\nhence eq will be  $(\\frac{5tan\\theta – 3}{5tan\\theta + 3})$
\nAs it is given that $5tan\\theta$ = 4
\nafter putting values and solving we will get the equation reduced to 1\/7.<\/p>\n

2) Answer (A)<\/strong><\/p>\n

$4sec^2\\theta+9cosec^2\\theta$
\nor $4+4tan^2\\theta+9+9cot^2\\theta$
\nor $13+4tan^2\\theta+9cot^2\\theta$
\nor $ 13+4tan^2\\theta+\\frac{9}{tan^2\\theta} $
\nor $  13-12+(2tan\\theta+\\frac{3}{tan\\theta})^2 $    (eq. (1) )
\nor now above expression to be minimum, equation $(2tan\\theta+\\frac{3}{tan\\theta})^2$ should be minimum.
\nSo applying $A.M.\\geq G.M. $
\n$\\frac{(2tan\\theta +\\frac{3}{tan\\theta})}{2} \\geq \\sqrt{6}$
\nor ${(2tan\\theta+\\frac{3}{tan\\theta})}=2\\sqrt{6}$ ( for value to be minimum)
\nAfter putting above value in eq.(1) , we will get least value of expression as 25.<\/p>\n

3) Answer (B)<\/strong><\/p>\n

$x=cosec\\theta – sin\\theta=\\frac{cos^2\\theta}{sin\\theta}=cot\\theta cos\\theta$
\nSimilarly $y=tan\\theta sin\\theta$
\n$xy=sin\\theta cos\\theta$
\n$x^2+y^2+3=(sec^2\\theta +cosec^2\\theta )$
\nNow putting above values in given equation, and after solving it will be reduced to 1<\/p>\n

4) Answer (A)<\/strong><\/p>\n

$2y=tan\\theta$
\n$x=2ycosec\\theta$
\nHence value of $x^2 – 4y^2 $ = $4y^2(cosec^2\\theta – 1)$
\nor $tan^2\\theta cot^2\\theta$ = 1<\/p>\n

5) Answer (A)<\/strong><\/p>\n

Given equation can be written as $(cos^4\\theta + cos^2\\theta)^3 -1$
\nas $sin\\theta + sin^2\\theta = 1$
\nor $sin\\theta = cos^2\\theta$
\nputting above value in given equation it will be
\n$(sin^2\\theta + sin\\theta)^3 -1 = 0$<\/p>\n

6) Answer (A)<\/strong><\/p>\n

$\\frac{sin\\theta}{1-cos\\theta} – \\frac{1}{sin\\theta}$<\/p>\n

or $\\frac{cos\\theta – cos^2\\theta}{(1-cos\\theta)sin\\theta}$ = $cot\\theta$<\/p>\n

7) Answer (C)<\/strong><\/p>\n

$\\sin^2 \\theta + \\cos^2 \\theta = 1$
\nSo, $\\sin^2 \\theta + \\cos^2 \\theta + 2\\sin\\theta * \\cos \\theta = 2 \\cos^2\\theta$
\nHence, $\\cos^2 \\theta – \\sin^2 \\theta = 2 \\sin\\theta*\\cos\\theta$
\nSo, $\\cos\\theta – \\sin\\theta = \\sqrt{2}\\sin\\theta$<\/p>\n

8) Answer (B)<\/strong><\/p>\n

$cos^4\\theta-sin^4\\theta=(cos^2\\theta-sin^2\\theta)(cos^2\\theta+sin^2\\theta)=cos^2\\theta-sin^2\\theta=\\frac{2}{3}$
\n$cos^2\\theta-sin^2\\theta =1-2sin^2\\theta=\\frac{2}{3}$<\/p>\n

9) Answer (A)<\/strong><\/p>\n

$\\frac{sin \\theta}{cos \\theta} = \\frac{3}{4}$
\nSo, $\\frac{sin^2\\theta}{cos^2\\theta}=\\frac{9}{16}$
\nHence, $sin^2 \\theta = \\frac{9}{9+16}=\\frac{9}{25}$
\nSo, $cosec \\theta = \\frac{5}{3}$<\/p>\n

10) Answer (A)<\/strong><\/p>\n

$1 + \\tan ^2 \\theta = \\sec ^2 \\theta$
\n$1 + \\cot ^2 \\theta = \\csc ^2 \\theta$
\nSo, the given fraction becomes,<\/p>\n

$\\frac{1}{\\sec ^2 \\theta} + \\frac{1}{\\csc ^2 \\theta} = \\sin^2\\theta + \\cos^2 \\theta = 1$<\/p>\n

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We hope this Trigonometry Questions for SSC  Exam preparation is so helpful to you.<\/p>\n","protected":false},"excerpt":{"rendered":"

SSC Questions on Trigonometry PDF Download SSC Trigonometry Questions with answers PDF based on previous papers very useful for SSC  exams. Top-10 Very Important Questions for SSC Exams. Take a free mock test for SSC CGL Download SSC CGL Previous Papers PDF More SSC CGL Important Questions and Answers PDF Question 1: $5tan\\theta = 4$, then […]<\/p>\n","protected":false},"author":49,"featured_media":40544,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3167,125,9,504,378,1493,1459,1611,1741,1441],"tags":[3638,165],"class_list":{"0":"post-40538","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-downloads-en","8":"category-featured","9":"category-ssc","10":"category-ssc-cgl","11":"category-ssc-chsl","12":"category-ssc-cpo","13":"category-ssc-gd","14":"category-ssc-je","15":"category-ssc-mts","16":"category-stenographer","17":"tag-questions-on-trigonometry","18":"tag-ssc"},"better_featured_image":{"id":40544,"alt_text":"SSC Questions on Trigonometry PDF","caption":"SSC 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