How do you verify the identity sin(90 + A) = cosA?

We have to prove sin (90 +A) = cos A

Solution

We know the trigonometric identity

sin (A + B) = sin A.cos B – sin B.cos A

Hence substituting A= 90 and B= A in the above identity. We get
sin (90 + A) = sin 90. cos A + sin A cos 90.
We have learnt that sin 90 = 1, And cos 90 = 0
sin (90 + A) = cos A