Answer :

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


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