Notes: Prove identity cos(x+2pi)=cosx

Saturday, June 6, 2015

Prove identity cos(x+2pi)=cosx

We'll apply the below identity to verify the given
expression:

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

Let a = x and b = 2 $\displaystyle\pi$

cos ( $\displaystyle{x}+{2}\pi$ ) = cos
x*cos $\displaystyle{2}\pi$ - sin $\displaystyle{2}\pi$ *sin x

But sin $\displaystyle{2}\pi$ = 0 and cos 2 =
1

cos (x+2 $\displaystyle\pi$ ) = cos x*1 - 0*sin x

cos (x +
2 $\displaystyle\pi$ ) = cos x

Therefore, the given identity cos
(x+2 $\displaystyle\pi$ ) = cos x is demonstrated.

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