Trigonometry Test for SSC CGL

If $\tan \theta + 3 \cot \theta - 2\sqrt{3} = 0$ and $0^\circ < \theta < 90^\circ$, then what is the value of $(\csc^2 \theta + \cos^2 \theta)$?

If $2k \sin 30^\circ \cos 30^\circ \cot 60^\circ = \frac{\cot^2 30^\circ \sec 60^\circ \tan 45^\circ}{\csc^2 45^\circ \csc 30^\circ}$, then find the value of $k$.

The value of $\frac{1 - 2\sin^2\theta\cos^2\theta}{\sin^4\theta + \cos^4\theta} - 1$ is:

If $\sec \theta = \frac{25}{24}$, then what is the value of $\sin \theta$?

The value of $\frac{\sec^2 60^\circ \cos^2 45^\circ + \csc^2 30^\circ }{\cot 30 ^\circ \sec^2 45 ^\circ - \csc^2 30 ^\circ \tan 45 ^\circ}$ is

If $6\tan A (\tan A + 1) = 5 - \tan A$, given that $0 < A < \frac{\pi}{2}$, what is the value of $(\sin A + \cos A)$?

If $0^\circ < \theta < 90^\circ$, $\sqrt{\frac{\sec^2 \theta + \csc^2 \theta}{\tan^2 \theta - \sin^2 \theta}}$ is equal to:

Find the value of $\tan 35^\circ \cot 40^\circ \tan 45^\circ \cot 50^\circ \tan 55^\circ$.

If $3\cos^2\theta - 4\sin\theta + 1 = 0$, $0^\circ < \theta < 90^\circ$, then $\tan\theta + \sec\theta = ?$

Simplify $\frac{(\sin \theta + \sec \theta)^2 + (\cos \theta + \csc \theta)^2}{(1 + \sec \theta \csc \theta)^2}$, where $0^\circ < \theta < 90^\circ$.