Question

$2\sin 45°\cos 45°=1$, how?

Answer 1

Show that$2\sin 45°\cos 45°=1$

$2\sin 45°\cos 45°=1$

$\begin{array}{rcl}\mathrm{LHS}& =& 2\sin 45°\cos 45°\\ & =& 2\times \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\left[\because \sin 45°=\cos 45°=\frac{1}{\sqrt{2}}\right]\\ & =& 2\times \frac{1}{2}\\ & =& 1.....\left(1\right)\\ \mathrm{RHS}& =& 1.......\left(2\right)\end{array}$

from$\left(1\right)$ and$\left(2\right)$,

$\therefore$$2\sin 45°\cos 45°=1$

Hence proved.