Question

Let $\sin 2A=\frac{4}{5}$ then find value of $\tan A$ for $0\le A\le \frac{\pi }{4}$.

Answer 1

Given,

$\sin 2A=\frac{4}{5}$

or, $\frac{2\tan A}{1+{\tan }^{2}A}=\frac{4}{5}$ [ Using formula of $\sin 2A$ in terms of $\tan A$]

or, $2{\tan }^{2}A-5\tan A+2=0$

or, $(2\tan A-1)(\tan A-2)=0$

Since $0\le A\le \frac{\pi }{4}$ then $\tan A=\frac{1}{2}$.