# Cos(-x) = Cos(x)

Why cos(-x)=cosx?Explain,please.

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### 2 Answers

Hi,

A geometric explanation is very intutive.

Look at sin(x) curve below. Sin(-1) = -Sin(1). it is not symmetric

But look at the cos(x) curve below. cos(-1) = cos(1). it is symmetric

We can write cos (-x) = cos (0-x), such as the following identity may now be used:

cos (a-b) = cos a*cos b + sin a*sin b

Let a = 0 and b = x

cos (0-x) = cos 0*cos x + sin 0*sin x

But cos 0 = 1 and sin 0 = 0.

cos (0 - x) = 1*cos x + 0*sin x

cos (0 - x) = cos x

**Therefore, the identity cos(-x) = cos x is verified.**