Equating sines

We know that answer is $sin^2x$ . So

$sin2x$ = $sin^2x$

Hence $2sin x cosx = sin^2x$

Hence $tanx = 2$

Now $sec^2x - tan^2x = 1$

$sec^2x = 5$

$cos^2x = 1/5$

$Sin^2x = 4/5$ $[Ans]$

$\sin^{2}{x}=\sin{(2x)}$

$\sin^{2}{x}=2\sin{x}\cos{x}$

$\sin{x}=2\cos{x}$

$\tan{x}=2$

$\cot{x}=\frac{1}{\tan{x}}=\frac{1}{2}$

$\sec^{2}{x}=\tan^{2}{x}+1=2^2+1=4+1=5$

$\csc^{2}{x}=\cot^{2}{x}+1=(\frac{1}{2})^2+1=\frac{1}{4}+1=\frac{1+4}{4}=\frac{5}{4}$

$\sec{x}=\sqrt{5}$ while $\csc{x}=\frac{\sqrt{5}}{2}$

$\cos{x}=\frac{1}{\sqrt{5}}$ while $\sin{x}=\frac{2}{\sqrt{5}}$

$\sin{2x}=2\sin{x}\cos{x}=\frac{2\times2}{5}=\frac{4}{5}$