If $\sin A=\frac{4}{5}$ and $\cos B=\frac{12}{13}$, Where both $A$ and $B$ lie in first quadrant. Find $\tan 2A$

Q.

(a) If $sinA=\frac{12}{13}$ and $sinB=\frac{4}{5},$ where $\frac{\pi }{2}<A<\pi$ and $0<B<\frac{\pi }{2},$ find the following:
(i) sin(A+B)
(ii) cos(A+B)
(b) If sinA= $\frac{3}{5}$, $cosB=\frac{12}{13}$, where A and B both lie in second quadrant, find the value of sin(A+B).

Q.

If sin A = $\frac{4}{5}$ and cos B = - $\frac{12}{13}$, where A and b lie in first

and third quadrant respectively, then cos(A + B) =

Q. (a) If $\sin A=\frac{12}{13}\mathrm{and}\sin B=\frac{4}{5}$, where $\frac{\mathrm{\pi }}{2}$< A < π and 0 < B < $\frac{\mathrm{\pi }}{2}$, find the following:

(i) sin (A + B)
(ii) cos (A + B)

(b) If $\sin A=\frac{3}{5},\cos B=-\frac{12}{13}$, where A and B both lie in second quadrant, find the value of sin (A + B).

Q. If $\cos A=\cos B=-\frac{1}{2}$ and $A$ does not lie in the second quadrant and $B$ does not lie in the third quadrant, then find the value of $\frac{4\sin B-3\tan A}{\tan B+\sin A}$