SSC Trigonometry questions

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

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

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?

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

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:

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:

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 :

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 $$\theta$$?

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

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

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:

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?

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:

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

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

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

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:

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

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:

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: