If $\sin \theta + \text{cosec} \theta = 2$,the value of $\sin^{10} \theta + \text{cosec}^{10} \theta$ is

If $\frac{x}{\cos \theta} = \frac{y}{\cos \left( \theta - \frac{2\pi}{3} \right)} = \frac{z}{\cos \left( \theta + \frac{2\pi}{3} \right)},$ then $x + y + z = $

Let $A, B, C$ be three angles such that $\sin A + \sin B + \sin C = 0$. Then,$\frac{\sin A \sin B \sin C}{\sin 3A + \sin 3B + \sin 3C}$ (wherever defined) is equal to:

In triangle $ABC$,the value of $\sin 2A + \sin 2B + \sin 2C$ is equal to

$\tan \theta \sin \left( \frac{\pi }{2} + \theta \right) \cos \left( \frac{\pi }{2} - \theta \right) = $

The value of $x$ for the maximum value of $\sqrt{3} \cos x + \sin x$ is .....$^o$