Prove: 2sin^2(45 - A) = 1 - 2sinA

Hey bud, the 45-A is nothing but just the angle. You can assume it as θ, solve the question, and substitute the original value at last.

Here is my solution without assuming angle as θ:

= 2sin²(45 - A)

we know that, cos2A = 1 - 2sin²A
so, 2sin²A = 1 - cos2A

= 1 - cos2(45 - A)
= 1 - cos(90 - 2A)

cos(90 - θ) is sinθ, so we can write,

= 1 - sin2A

We got our required answer! And below is the video explanation: