Question

Prove this identify : 2 cos^2 (45°-A ) = 1 +sin 2 A​

Answer 1

I am guessing that you mean 2cos2(45° - x) = 1 + sin2x

According to a double angle identity, 2cos2θ - 1 = cos(2θ)

So, 2cos2(45° - x) - 1 = cos (90° - 2x)

= cos90°cos2x + sin90°sin2x

= (0)cos2x + (1)sin2x

= sin2x

Thus, 2cos2(45° - x) = 1 + sin2x