If $\tan \theta - \cot \theta = a$ and $\sin \theta + \cos \theta = b,$ then ${({b^2} - 1)^2}({a^2} + 4)$ is equal to
$2$
$-4$
$± 4$
$4$
If $\tan \theta = \frac{{x\,\sin \,\phi }}{{1 - x\,\cos \,\phi }}$ and $\tan \,\phi = \frac{{y\sin \,\theta }}{{1 - y\,\cos \,\theta }}$, then $\frac{x}{y} = $
Prove that $\cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-x\right)=-\sqrt{2} \sin x$
If $\sin x + {\sin ^2}x = 1,$ then ${\cos ^8}x + 2{\cos ^6}x + {\cos ^4}x = $
The value of $\sin 10^\circ + \sin 20^\circ + \sin 30^\circ + ... + $ $\sin 360^\circ $ is
Prove that: $(\cos x-\cos y)^{2}+(\sin x-\sin y)^{2}=4 \sin ^{2} \frac{x-y}{2}$