The simplified form of the given expression $\sin A \cos A(\tan A - \cot A)$ is (where $0^{\circ} \leq A \leq 90^{\circ}$)

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 $\frac{\tan x}{\tan 3x}$,whenever defined,never lies between:

If $\alpha, \beta, \gamma, \delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$,then the value of $4\sin \frac{\alpha}{2} + 3\sin \frac{\beta}{2} + 2\sin \frac{\gamma}{2} + \sin \frac{\delta}{2}$ is equal to

$\frac{\sin 3\theta + \sin 5\theta + \sin 7\theta + \sin 9\theta}{\cos 3\theta + \cos 5\theta + \cos 7\theta + \cos 9\theta} = $

If $\sin x + \sin^2 x = 1,$ then $\cos^8 x + 2\cos^6 x + \cos^4 x = $