The value of $6({\sin ^6}\theta + {\cos ^6}\theta ) - 9({\sin ^4}\theta + {\cos ^4}\theta ) + 4$ is
$-3$
$0$
$1$
$3$
The equation ${(a + b)^2} = 4ab\,{\sin ^2}\theta $ is possible only when
Find the values of other five trigonometric functions if $\cos x=-\frac{1}{2}, x$ lies in third quadrant.
Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6: 15$ the difference between these two angles is $....^{\circ}$
If $2y\,\cos \theta = x\sin \,\theta {\rm{ and }}2x\sec \theta - y\,{\rm{cosec}}\,\theta = 3,$ then ${x^2} + 4{y^2} = $
Prove that: $(\cos x+\cos y)^{2}+(\sin x-\sin y)^{2}=4 \cos ^{2} \frac{x+y}{2}$