Question

If $4\sin A=3\cos A$ then evaluate $\sin 2A$.

Answer 1

Given,

$\Rightarrow 4\sin A=3\cos A$

$\Rightarrow \frac{\sin A}{\cos A}=\frac{3}{4}$

$\Rightarrow \tan A=\frac{3}{4}$

Now,

$\Rightarrow \sin 2A$

$\Rightarrow \frac{2\tan A}{1+{\tan }^{2}A}$ putting $\tan A=\frac{3}{4}$

$\Rightarrow \frac{2\times \frac{3}{4}}{1+\frac{9}{16}}$

$\Rightarrow \frac{\frac{3}{2}}{\frac{16+9}{16}}$

$=\frac{3}{2}\times \frac{16}{25}$

$\Rightarrow \frac{24}{25}$.