Question

Prove the following:
If $\tan A=\frac{3}{4}$ , then $\sin A\cos A=\frac{12}{25}$

Answer 1

$\tan A=\frac{3}{4}\therefore \sin A.\cos A=\frac{2}{2}\sin A.\cos A=\frac{\sin 2A}{2}=\frac{1}{2}\frac{2\tan A}{1+\tan {}^{2}A}=\frac{\frac{3}{4}}{1+\frac{9}{16}}=\frac{\frac{3}{4}}{\frac{25}{16}}=\frac{12}{25}=RHS$