Question

Find the value of $x$ (in deg.) , if $\sin 2x$ = $\sin {60}^{\circ }\cos {30}^{\circ }-\cos {60}^{\circ }\sin {30}^{\circ }$

Answer 1

$sin2x=sin60cos30-cos60sin30$
$sin2x=\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}-\frac{1}{2}\times \frac{1}{2}$
$sin2x=\frac{3}{4}-\frac{1}{4}$
$sin2x=\frac{1}{2}$
$sin2x=sin30$
$2x=30$
$x={15}^{\circ }$