If $\cos A = \frac{\sqrt{3}}{2},$ then $\tan 3A = $

If $3 \sin \theta + 5 \cos \theta = 5$,then the value of $5 \sin \theta - 3 \cos \theta$ will be

$(\sec 2A + 1){\sec ^2}A = $

If $\cot \theta + \cos \theta = p$ and $\cot \theta - \cos \theta = q$,then $(p^2 - q^2)^2$ in terms of $p$ and $q$ is: (in $pq$)

The value of $\frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$ is equal to:

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $ax^2 + bx + c = 0$ $(c \neq 0)$,then: