We need to find the value of:

Let

Take cosine on both sides, we get

Using property of inverse trigonometry,

cos(cos^-1 A) = A

We have the value of cos x, let us find the value of sin x.

By trigonometric identity,

sin² x + cos² x = 1

⇒ sin² x = 1 – cos² x

Putting ,

Now,

Using the trigonometric identity,

sin 2x = 2 sin x cos x

Putting the value of and ,