I need help to prove identity sin(x+2pi)=sinx

Asked on by gateau66

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll have to use the following formula in order to prove the given expression:

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

Let a = x and b = 2`pi`

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

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

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

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

Therefore, the given identity sin (x+2`pi` ) = sin x is verified.

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