Question

Evaluate:$\cos 60°\times \cos 30°+\sin 60°\times \sin 30°$

Answer 1

Given that $\cos 60°\times \cos 30°+\sin 60°\times \sin 30°$

Formula used $\left[\mathrm{Cos}\right(\mathrm{A}-\mathrm{B})=\mathrm{CosACosB}+\mathrm{SinASinB}]$

$\cos 60°\times \cos 30°+\sin 60°\times \sin 30°$$=\cos ({60}^0-{30}^0)$

$=\cos {30}^0$

$=\frac{\sqrt{3}}{\sqrt{2}}$ $(\cos {30}^0=\frac{\surd 3}{2})$

Thus, $\cos 60°\times \cos 30°+\sin 60°\times \sin 30°$$=\frac{\sqrt{3}}{\sqrt{2}}$