If $\tan A = \frac{1 - \cos B}{\sin B},$ find $\tan 2A$ in terms of $\tan B$.

If $\cos \theta = \frac{-3}{5}$ and $\theta$ does not lie in the second quadrant,then $\tan \frac{\theta}{2} = $

The value of $\cos 15^{\circ} \cos 7.5^{\circ} \sin 7.5^{\circ}$ is

If $\frac{\sec 8\theta - 1}{\sec 4\theta - 1} = \frac{a + b \tan^2 2\theta}{1 + c \tan^2 2\theta + d \tan^4 2\theta}$ (where $\theta \neq \frac{n\pi}{16}, n \in I$),then the value of $(a - b + c - d)$ is -

If $\cos A = \frac{3}{4}$,then $32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5A}{2}\right) = $

The value of $\tan \frac{\pi}{8}$ is equal to