If $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha $and $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha $, then $\theta$ is equal to
$\alpha /2$
$\alpha $
$2\alpha $
$\alpha /6$
$\tan 75^\circ - \cot 75^\circ = $
The value of $x$ that satisfies the relation $x = 1 - x + x^2 - x^3 + x^4 - x^5 + ......... \infty$
The value of $\frac{{3 + \cot {{76}^o}\cot {{16}^o}}}{{\cot {{76}^o} + \cot {{16}^o}}}$
The value of $ \cos ^{3}\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^{3}\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right)$ is
If $\sin \theta+\cos \theta=\frac{1}{2}$, then $16(\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta))$ is equal to: