The minimum value of $3\sin \theta + 4\cos \theta$ is

If $\sin \theta = \frac{12}{13}$ where $0 < \theta < \frac{\pi}{2}$ and $\cos \phi = -\frac{3}{5}$ where $\pi < \phi < \frac{3\pi}{2}$,then $\sin(\theta + \phi)$ is:

If $\sqrt{2} \tan 2 \theta = \sqrt{6}$ and $0^{\circ} < \theta < 45^{\circ},$ then the value of $\sin \theta + \sqrt{3} \cos \theta - 2 \tan^{2} \theta$ is

The maximum value of $f(x) = \sin x + \cos x$ is

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

If $\sin \theta = \frac{3}{5},$ then the value of $\frac{\tan \theta + \cos \theta}{\cot \theta + \operatorname{cosec} \theta}$ is equal to