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Prove that cos 2x + 2sin^2x = 1

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Prove that

cos 2x + 2sin2x = 1

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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 [∵ cos2θ + sin2θ = 1]

= 2 – 1

= 1

= RHS

∴ LHS = RHS

Hence Proved

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