Question

The value of $x$ satisfying the equation $\cos 2x=\cos {60}^o\cos {30}^o+\sin {60}^o\sin {30}^o$ is

Answer 1

$\cos 2x=\cos {60}^o\cos {30}^o+\sin {60}^o\sin {30}^o$

$\cos 2x=\frac{1}{2}\times \frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}\times \frac{1}{2}$

$\cos 2x=\frac{\sqrt{3}}{4}+\frac{\sqrt{3}}{4}=\frac{\sqrt{3}}{2}$

$\cos 2x=\cos {30}^o$

$2x={30}^o$

$x={15}^o$