If $\tanh x=\operatorname{sech} y=\frac{3}{5}$ and $e^{x+y}$ is an integer, then $e^{x+ y}$ =

If $A, B, C$ are the angles of triangle, then $\sin 2 A-\sin 2 B+\sin 2 C=$

Assertion (A) : If $A=10^{\circ}, B=16^{\circ}$ and $C=19^{\circ}$, then $\tan 2 A \tan 2 B+\tan 2 B \tan 2 C+\tan 2 C \tan 2 A=1$

Reason (R) : If $A+B+C=180^{\circ}, \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}$

$$ =\cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} $$

Which of the following is correct ?

If $\alpha$ is in the 3rd quadrant, $\beta$ is in the 2nd quadrant such that $\tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}$, then $\sin (2 \alpha+\beta)=$