$\cot 5^o - \tan 5^o - 2 \tan 10^o - 4 \tan 20^o - 8 \cot 40^o$ is equal to

If $\tan \frac{\theta}{2} = t$,then $\frac{1 - t^2}{1 + t^2}$ is equal to

If $3 \sin x + 4 \cos x = 5$,then $6 \tan \frac{x}{2} - 9 \tan^2 \frac{x}{2}$ is equal to

$\operatorname{cosec} 2 \theta - \cot 2 \theta = ?$

If $\left(\frac{\sin 3 \theta}{\sin \theta}\right)^2-\left(\frac{\cos 3 \theta}{\cos \theta}\right)^2=a \cos b \theta$,then $a: b=$

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 -