To Prove: cos 2x + 2sin²x = 1

Taking LHS,

= cos 2x + 2sin²x

= (2cos²x – 1) + 2sin²x [∵ 1 + cos 2x = 2 cos²x]

= 2(cos²x + sin²x) – 1

= 2(1) – 1 [∵ cos² θ + sin² θ = 1]

= 2 – 1

= 1

= RHS

∴ LHS = RHS

Hence Proved