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

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.