What is the value of $\frac{[\sin (y-z)+\sin (y+z)+2 \sin y]}{[\sin (x-z)+\sin (x+z)+2 \sin x]} = ?$

$\frac{\sec 8\theta - 1}{\sec 4\theta - 1}$ is equal to

If $A = \cos^2 \theta + \sin^4 \theta$,then for all values of $\theta$:

For any $\theta \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$,the expression $3(\sin \theta - \cos \theta)^4 + 6(\sin \theta + \cos \theta)^2 + 4\sin^6 \theta$ equals

The value of $x,$ which satisfies the equation $2 \operatorname{cosec}^{2} 30^{\circ} + x \sin^{2} 60^{\circ} - \frac{3}{4} \tan^{2} 30^{\circ} = 10$ is

$(\sec A + \tan A - 1)(\sec A - \tan A + 1) - 2\tan A = $