Question

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

Answer 1

$\to$ given $\sin A=\frac{4}{5}$ and $\cos B=\frac{12}{13};A$ and $B$ are in first Quadrant.

$\therefore \tan 2A=\frac{2\tan A}{1-{\tan }^{2}A}$

As $\sin A=\frac{4}{5}\Rightarrow \tan A=\frac{4}{3}$

$\Rightarrow \tan 2A=\frac{2\times \frac{4}{3}}{1-\frac{16}{9}}=\frac{\frac{8}{3}}{\frac{-7}{9}}=\frac{8}{3}\times \frac{-9}{7}=\frac{-24}{7}$

$\therefore \tan 2A=\frac{-24}{7}$