SSC Trigonometry Questions with Answers

Trigonometry

An excellent collection of SSC Trigonometry questions and answers with detailed explanations for competitive exams. Given below are some of the most repeated practice questions on Trigonometry for SSC CGL, CHSL, JE, GD constable, Stenographer, MTS, and CPO exams. Go through this very important online quiz based on model and previous year asked questions from SSC Trigonometry with solutions to ace the exam.

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Instructions

For the following questions answer them individually

Question 1

P and Q are two points observed from the top of a building 10√3 m high. If the angles of depression of the points are complementary and PQ = 20m, then the distance of P from the building is

Question 2

A person of height 6ft. wants to pluck a fruit which is on a 26/3 ft. high tree. If the person is standing 8/√3 ft. away from the base of the tree, then at what angle should he throw a stone so that it hits the fruit ?

Question 3

If θ is an acute angle and $$\tan^2\theta+\frac{1}{\tan^2\theta}=2$$ then the value of θ is :

Question 4

If $$\frac{\cos\alpha}{\sin\beta}=n$$ and $$\frac{\cos\alpha}{\cos\beta}=m$$ then the value of $$\cos^{2} \beta$$ is

Question 5

What is the simplified value of $$cosec2A + cot2A$$ ?

Question 6

The value of $$\frac{sin 43^{\circ}}{cos 47^{\circ}}+\frac{cos 19^{\circ}}{sin 71^{\circ}}-8cos^{2}60^{\circ}$$ is

Question 7

The angle of elevation of a tower from a distance of 100 metre from its foot is 30°. Then the height of the tower is

Question 8

$$5tan\theta = 4$$, then the value of $$(\frac{5sin\theta - 3cos\theta}{5sin\theta + 3cos\theta})$$ is

Question 9

If p sin θ = √3 and p cos θ = 1, then the value of p is :

Question 10

If $$sin θ + sin^{2} θ = 1$$ then $$cos^2 θ + cos^4 θ$$ is equal to

Question 11

If tan θ + cot θ = 5, then $$tan^2 θ + cot^2 θ$$ is

Question 12

If 0° ≤ A ≤ 90°, the simplified form of the given expression sin A cos A (tan A - cot A) is

Question 13

The numerical value of $$\frac{cos^2 45\circ}{sin^2 60\circ}+\frac{cos^2 60\circ}{sin^2 45\circ}-\frac{tan^230\circ}{cot^245\circ}-\frac{sin^230\circ}{cot^230\circ}$$ is

Question 14

The value of tan1°tan2°tan3° ……………tan89° is

Question 15

If sin 2θ =1/2, then the value of cos (75°­ - θ) is :

Question 16

If cot A + cosec A = 3 and A is an acute angle, then the value of cos A is :

Question 17

$$1 - \frac{sin^2 A}{1 + cos A} + \frac{1 + cos A}{sin A} - \frac{sin A}{1 - cos A}$$

Question 18

Find the value of tan 4° tan 43° tan 47 tan 86°

Question 19

If θ be acute angle and tan (4θ - 50°) = cot(50° - θ), then the value of 9 in degrees is:

Question 20

The value of $$sin^{2}$$ 22° + $$sin^{2}$$ 68° + $$cot^{2}$$ 30° is

Question 21

If the number of vertices, edges and faces of a rectangualr parallelopiped are denoted by v, e and f respectively, the value of (v - e + f) is

Question 22

A kite is flying at the height of 75m from the ground. The string makes an angle θ (where cotθ = 8/15) with the level ground. Assuming that there is no slack in the string the length of the string is equal to :

Question 23

If $$\alpha$$ is a positive acute angle and $$2sin\alpha + 15cos^{2}\alpha = 7$$, then the value of cota is:2

Question 24

If (a^2 - ­b^2) sin θ + 2 ab cosθ = a^2 + b^2, then the value of tanθ is

Question 25

If tanθ - cotθ = α and cosθ sinθ = b, then the value of (a^2 + 4) (b^2 - ­1)^2 is:

Question 26

The least value of 4cosec^2 α + 9sin^2 α is:

Question 27

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

Question 28

The maximum value of sin θ + cos θ is

Question 29

If tan $$\theta$$ + cot $$\theta$$ = 2 then the value of $$\theta$$ is

Question 30

If $$sin\theta + \sin^2\theta = 1$$, then the value of cos12$$\theta$$ + 3cos10$$\theta$$ + cos6$$\theta$$ +  3cos8$$\theta$$  - 1 is

Question 31

If secθ + tanθ = p, (p ≠ 0) then secθ is equal to

Question 32

If 0 ≤ α ≤ π/2 and 2sinα + 15 cos^2 α = 7 then the value of cot α is :

Question 33

If $$u_n = cos^n α + sin^n α$$, then the value of $$2u_6 - 3u_4 +1$$ is :

Question 34

If tan(x + y) tan(x - y) = 1, then the value of tan x is :

Question 35

If sin (x + y) = cos [3(x + y)], then the value of tan[2(x + y)] is :

Question 36

From the top of a cliff 90 metre high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is :

Question 37

If A = 30°, B = 60° and C = 135°, then what is the value of $$sin^3A + cos^3B + tan^3C - 3sin A cos B tan C$$ ?

Question 38

The minimum value of $$2sin^{2}$$ θ + $$3cos^{2}$$ θ is

Question 39

A boy standing in the middle of a field, observes a flying bird in the north at an angle of elevation of 30° and after 2 minutes, he observes the same bird in the south at an angle of elevation of 60°. If the bird flies all along in a straight line at a height of 50 m, then its speed in km/h is :

Question 40

The value of (1 + sec 20° + cot 70°) * (1 - cosec 20° + tan 70°) is ?

Question 41

If x*sin^3 θ + y *cos^3 θ = sinθ * cosθ ≠ 0 and x sinθ - y cosθ = 0, then value of (x^2 + y^2 ) is

Question 42

If secθ - cosecθ = 0, then the value of (secθ + cosecθ) is :

Question 43

If $$x=cosec\theta-sin\theta$$ and $$y=sec\theta-cos\theta$$, then the value of $$x2y2(x2 + y2 + 3)$$

Question 44

The least value of $$(4sec^2\theta + 9cosec^2\theta)$$ is

Question 45

What is the least value of $$tan^2θ + cot^2θ + sin^2θ + cos^2θ + sec^2θ + cosec^2θ$$ ?

Question 46

What is the value of $$(\frac{2}{\sqrt{3}}+tan45^\circ)$$ ?

Question 47

If $$sin\frac{\pi{x}}{2}=x^{2}-2x+2$$, then the value of x is

Question 48

The numerical value of $$1+\frac{1}{\cot^{2}63^{\circ}}-\sec^{2}27^{\circ}+\frac{1}{\sin^{2}63^{\circ}}-cosec^{2}27^{\circ}$$ is

Question 49

If $$\cos\pi$$x$$=x^{2}-x+\frac{5}{4}$$ the value ue of x will be

Question 50

In a right ­angled triangle ABC, ∠B is the right angle and AC = 2√5­ cm. If AB - BC = 2 cm then the value of $$(cos^2 A - cos^2 C)$$ is :

Question 51

If $$x cosθ - sinθ = 1,$$ then $$x^{2} - (1 +x^{2}) sinθ$$ equals

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