Verify the identity. sin(x + y) - sin(x - y) = 2 cosx siny

Solution:

Given sin(x + y) - sin(x - y)

Here, we are using the following trignometric identitites:

sin(A + B) = sinAcosB + sinBcosA

sin(A - B) = sinAcosB - sinBcosA

Hence,sin(x + y) - sin(x - y) = sinxcosy + sinycosx - (sinxcosy - sinycosx)

sin(x + y) - sin(x - y) = sinxcosy + sinycosx - sinxcosy + sinycosx

sin(x + y) - sin(x - y) = sinxcosy + sinycosx - sinxcosy + sinycosx

sin(x + y) - sin(x - y) = sinycosx + sinycosx

sin(x + y) - sin(x - y) = 2sinycosx

Hence verified.

Verify the identity. sin (x + y) - sin (x - y) = 2 cos x sin y

Summary:

The equation sin (x + y) - sin (x - y) = 2 cos x sin y is verified.