If $\sin 2\theta + \sin 2\phi = 1/2$ and $\cos 2\theta + \cos 2\phi = 3/2$, then ${\cos ^2}(\theta - \phi ) = $
$3/8$
$5/8$
$3/4$
$5/4$
$\sqrt {2 + \sqrt {2 + 2\cos 4\theta } } = $
Prove that $=\frac{\sin 5 x-2 \sin 3 x+\sin x}{\cos 5 x-\cos x}=\tan x$
If a $cos^3 \alpha + 3a \,cos\, \alpha \, sin^2\, \alpha = m$ and $asin^3\, \alpha + 3a \, cos^2\, \alpha \,sin\, \alpha = n$ . Then $(m + n)^{2/3} + (m - n)^{2/3}$ is equal to :
The value of $\sum_{r-1}^{18} cos^2(5r)^o,$ where $x^o $ denotes the $x$ degree, is equals to
$\tan \frac{A}{2}$ is equal to