Question

11. Find the value of x in the following:
(i) cos x = cos 60° cos 30° + sin 60° sin 30°​

Answer 1

Step-by-step explanation:

it is

$\frac{ \sqrt{3} }{2}$

Answer 2

Answer:

$x=30^\circ$ or $x=\frac{\pi}{6}$

Step-by-step explanation:

Since

$\cos (A-B)=\cos A\cos B+\sin A\sin B$

Substitute $A=60^\circ$ and $B=30^\circ$

$\cos (60^\circ-30^\circ)=\cos 60^\circ\cos 30^\circ+\sin 60^\circ\sin 30^\circ$

$\cos 30^\circ=\cos 60^\circ\cos 30^\circ+\sin 60^\circ\sin 30^\circ$

$\cos 30^\circ=\cos x$

$\cos x=\cos 30^\circ$

$x=\cos^{-1}\cos{30^\circ}$

$x=30^\circ$

Therefore,

$x=30^\circ$ or $x=\frac{\pi}{6}$