The maximum value of the expression $E = \sin \theta + \cos \theta + \sin 2\theta$ is-

For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval:

If $A + B + C = 180^o$,then the value of $\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}$ is equal to

If $\cos A \sin \left( A - \frac{\pi}{6} \right)$ is maximum,then the value of $A$ is equal to

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^2$,where $f(\theta)=\sqrt{a^2 \cos^2 \theta+b^2 \sin^2 \theta} + \sqrt{a^2 \sin^2 \theta+b^2 \cos^2 \theta}$. Then $M-m=$

Assertion $(A)$: If $\alpha=12^{\circ}, \beta=15^{\circ}, \gamma=18^{\circ}$,then $\tan 2 \alpha \tan 2 \beta+\tan 2 \beta \tan 2 \gamma+\tan 2 \gamma \tan 2 \alpha=1$.
Reason $(R)$: In $\triangle ABC$,$\tan \frac{A}{2} \tan \frac{B}{2}+\tan \frac{B}{2} \tan \frac{C}{2}+\tan \frac{C}{2} \tan \frac{A}{2}=1$.
Which of the following is true?