# Prove that the cosine of double angle may be written in terms of sine of angle.

### 1 Answer | Add Yours

We'll write the cosine of double angle as cos 2x. We know that the cosine of double angle can be written as as the cosine of the sum of 2 like angles:

cos(x+x) = cos x*cos x - sin x*sin x

cos(x+x) = (cos x)^2 - (sin x)^2 (1)

We'll write cos x in terms of sin x, applying the fundamental formula of trigonometry:

(sin x)^2 + (cosx)^2 = 1

(cos x)^2 = 1 - (sin x)^2 (2)

We'll substitute (2) in (1):

cos(x+x) = (cos x)^2 - [1 - (cos x)^2]]

We'll remove the brackets:

cos 2x = 1 - (sin x)^2 - (sin x)^2

We'll combine like terms:

cos 2x = 1 - 2(sin x)^2

So,the expression of cos 2x, written in terms of sin x, is:

**cos 2x = 1 - 2(sin x)^2**