SSC Trigonometry questions

SSC 2022 Trigonometry questions

Question 1

If $$\tan B = \frac{5}{3}$$, what is the value of $$\frac{\cosec B + \sin B}{\cos B - \sec B}$$?

Question 2

If $$6 \tan A \left(\tan A - 1\right) = 5 - \tan A$$, Given that O < A < $$\frac{\pi}{2}$$. what is the value of $$\left(\sin A + \cos A\right)$$?

SSC 2021 Trigonometry questions

Question 1

A ladder leaning against a wall makes an angle $$\theta$$ with the horizontal ground such that $$\tan \theta = \frac{12}{5}.$$ If the height of the top of the ladder from the wall is 24 m, then what is the distance (in m) of the foot of the ladder from the wall?

Question 2

$$\frac{\sin^2 52^\circ + 2 + \sin^{2} 38^\circ}{4 \cos^{2} 43^\circ - 5 + 4 \cos^{2} 47^\circ}$$ is:

Question 3

ladder is resting against a wall. The angle between the foot of the ladder and wall is $$60^\circ$$, and the foot of the ladder is 3.6 m away from the wall. The length of the ladder (in m) is:

Question 4

If $$4(cosec^2 57 - \tan^2 33) - \cos 90 + y * \tan^2 66 * \tan^2 24 = \frac{y}{2}$$, then the value of y is:

Question 5

Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are $$30^\circ$$ and $$45^\circ$$, respectively. The ratio of the heights of A and B is :

Question 6

If $$4 \theta$$ is an acute angle , and $$\cot 4 \theta = \tan(\theta - 5^\circ)$$ is an acute angle, and $$\cot 46 = \tan(6 - 5^\circ)$$, then what is the value of $$\theta$$?

Question 7

If $$4 - 2 \sin^2 \theta - 5 \cos \theta = 0, 0^\circ < \theta < 90^\circ$$, then the value of $$\cos \theta - \tan \theta$$ is:

Question 8

Solve for $$\theta: \cos^{2} - \sin^{2} \theta = \frac{1}{2}, 0 < \theta < 90^\circ$$.

Question 9

If $$\cot \theta = \frac{1}{\sqrt{3}}, 0^\circ < \theta^\circ < 90^\circ$$ then the value of $$\frac{2 - \sin^{2} \theta}{1 - \cos^{2} \theta} + (\cosec^{2} \theta - \sec \theta)$$ is:

Question 10

A person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall?

Question 11

Let A and B be two towers with same base. From the midpoint of the line joining their feet. the angles of elevation of the tops of A and B are $$30^\circ$$ and $$60^\circ$$, respectively. The ratio of the heights of B and A is:

Question 12

What is the average of sixty terms given below?
$$\cos^{2}x$$, $$\cos^{2}2x \cos^{2}3x$$,... $$\cos^{2}30x$$, $$\sin^{2}x$$, $$\sin^{2}2x$$, $$\sin^{2}3x$$,... $$\sin^{2}30x$$

Question 13

If $$3 \sin^2 \theta - \cos \theta - 1 = 0, 0^\circ < \theta < 90^\circ$$, then what is the value of $$\cot \theta + \cosec \theta ?$$

Question 14

If $$\sin A = \frac{1}{2}, A$$ is an acute angle, then find the value of $$\frac{\tan A - \cot A}{\sqrt{3}(1 + \cosec A)}$$

Question 15

If $$\frac{\cos^2 \theta}{\cot^2 \theta + \sin^2 \theta - 1} = 3, 0^\circ < \theta < 90^\circ$$, then the value of $$(\tan \theta + \cosec \theta)$$ is:

Question 16

$$1 + 2 \tan^2 \theta + 2 \sin \theta \sec^2 \theta, 0^\circ < \theta < 90^\circ$$, is equal to:

Question 17

If $$\frac{\sin^2 \theta}{\tan^2 \theta - \sin^2 \theta} = 5, \theta$$ is an acute angle, then the value of $$\frac{24\sin^2\theta-15\sec^2\theta}{6\operatorname{cosec}^2\theta-7\cot^2\theta}$$ is:

Question 18

If $$\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=5$$, then the value of $$\frac{4\sin^2\theta+3}{2\cos^2\theta+2}$$ is: