Prove identity cos(x+2pi)=cosx

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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`pi`

cos (`x+ 2pi` ) = cos x*cos `2pi` - sin `2pi` *sin x

But sin `2pi` = 0 and cos 2 = 1

cos (x+2`pi` ) = cos x*1 - 0*sin x

cos (x + 2`pi` ) = cos x

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

lochana2500's profile pic

lochana2500 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

cos(x+2π) = cosx.cos2π - sinx.sin2π

we know that cos2π=1 and sin2π=0

= cosx.1 - sinx.0

= cosx

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