If $y = 3\,\sin\,x + 4\,\cos\,x$,then find the maximum value of $y$.

If $180^{\circ} < \theta < 270^{\circ},$ then the value of $\sqrt{4 \sin^{4} \theta + \sin^{2} 2\theta} + 4 \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

If $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ ,$ then the value of $x$ is

$\cos 20^\circ \cos 40^\circ \cos 80^\circ = $

In a triangle $ABC,$ the value of $\sin A + \sin B + \sin C$ is

If $\tan \left( \frac{\pi}{4} + \theta \right) + \tan \left( \frac{\pi}{4} - \theta \right) = \lambda \sec 2\theta$,then $\lambda$ =