Show that sin(pi/2-x)=cosx?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll have to apply the following identity to prove the given expression:

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

Let a = `pi` /2 and b = x

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

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

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

sin (`pi` /2 - x) = cos x

Therefore, the given expression sin (`pi` /2 - x) = cos x represents an identity.

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