If $x{\sin ^3}\alpha + y{\cos ^3}\alpha = \sin \alpha \cos \alpha $ and $x\sin \alpha - y\cos \alpha = 0,$ then ${x^2} + {y^2} = $
$-1$
$±1$
$1$
None of these
The value of ${\sin ^2}{5^o} + {\sin ^2}{10^o} + {\sin ^2}{15^o} + ... + $ ${\sin ^2}{85^o} + {\sin ^2}{90^o}$ is equal to
If $p = \frac{{2\sin \,\theta }}{{1 + \cos \theta + \sin \theta }}$, and $q = \frac{{\cos \theta }}{{1 + \sin \theta }},$ then
If $\sin \theta + {\rm{cosec}}\theta = 2,$ the value of ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ is
Prove that:
$ 2 \cos \frac{\pi}{13} \cos \frac{9 \pi}{13}+\cos \frac{3 \pi}{13}+\cos \frac{5 \pi}{13}=0$
The equation ${\sin ^2}\theta = \frac{{{x^2} + {y^2}}}{{2xy}},x,y, \ne 0$ is possible if