There is a mistake in the equation you provided. The correct identity should be:

sin^2(a) + cos^2(a) = 1

Now, let's simplify the right side of the equation:

1/8 sin(4a) = 1/8 2sin(2a)cos(2a)
= 1/4 sin(2a)cos(2a)
= 1/4 (1/2 sin(4a))
= 1/8 sin(4a)

Therefore, the correct equation should be:

sin^2(a) + cos^2(a) = 1/8 sin(4a)

This identity is true based on trigonometric identities.