If one solution of the equation $\cosh x - \frac{4}{5} \sinh x = 1$ is $x = 0$,then the other solution is $x =$

Evaluate the product: $\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{2 \pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{4 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{6 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right)$

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

If $\tan(\pi \sin \theta) = \cot(\pi \cos \theta)$,then $\left| \cot \left( \theta - \frac{\pi}{4} \right) \right|$ is -

Consider the following parametric equation of a curve: $x(\theta) = |\cos 4\theta| \cos \theta$ and $y(\theta) = |\cos 4\theta| \sin \theta$,where $0 \leq \theta \leq 2\pi$. Which one of the following graphs represents the curve?

Evaluate: $\sqrt{3} \operatorname{cosec} 20^{\circ} - \sec 20^{\circ}$