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.
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.