All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in :

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

Let $S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^2 \theta}+8^{20 \cos ^2 \theta}=16\right\}$. Then $n(S)+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is equal to .

A tower $P Q$ stands on a horizontal ground with base $Q$ on the ground. The point $R$ divides the tower in two parts such...

The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is in

$\alpha=\sin 36^{\circ}$ is a root of which of the following equation

The number of solutions of the equation $\sin x=\cos ^2 x$ in the interval $(0,10)$ is $\_\_\_\_$ .

If $\cot \alpha=1$ and $\sec \beta=-\frac{5}{3}$, where $\pi<\alpha<\frac{3 \pi}{2}$ and $\frac{\pi}{2}<\beta<\pi$, then the value of $\tan (\alpha+\beta)$ and the quadrant in which $\alpha+\beta$ lies, respectively...

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends...