The number of solutions of the equation $32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ is :

If ${\sin ^2}\theta = \frac{1}{4},$ then the most general value of $\theta $ is

Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -

The most general value of $\theta $ satisfying the equations $\tan \theta = - 1$ and $\cos \theta = \frac{1}{{\sqrt 2 }}$ is

Let $S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$. Then the number of elements in the set $=\{\theta \in S : \tan \theta(1+\sqrt{5} \tan (2 \theta))=\sqrt{5}-\tan (2 \theta)\}$ is $...$

Find the general solution of the equation $\cos 3 x+\cos x-\cos 2 x=0$