Question

$\cos {60}^0\times \cos {30}^0-\sin {60}^0\times \sin {30}^0$ = 0

Answer 1

$\cos {60}^o\times \cos {30}^o-\sin {60}^o\times \sin {30}^o$

We know that

$\sin {60}^o=\frac{\sqrt{3}}{2},\sin {30}^o=\frac{1}{2}$

$\cos {60}^o=\frac{1}{2},\cos {30}^o=\frac{\sqrt{3}}{2}$

$\cos {60}^o\times \cos {30}^o-\sin {60}^o\times \sin {30}^o$

$=\frac{1}{2}\left(\frac{\sqrt{3}}{2}\right)-\frac{\sqrt{3}}{2}\left(\frac{1}{2}\right)$

$=\frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}=0$

$\therefore \cos {60}^o\times \cos {30}^o-\sin {60}^o\times \sin {30}^o=0$