Question

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

Answer 1

I am guessing that you mean 2cos2(45° - A) = 1 + sin2A

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

So, 2cos2(45° - A) - 1

= cos (90° - 2A) =cos90°cos2A + sin90°sin2A = (0)cos2A + (1)sin2A = sin2

Thus, 2cos2(45° -A ) = 1 + sin2A