Q. 114.0( 4 Votes )

# Prove that

cos 2x + 2sin^{2}x = 1

Answer :

To Prove: cos 2x + 2sin^{2}x = 1

Taking LHS,

= cos 2x + 2sin^{2}x

= (2cos^{2}x – 1) + 2sin^{2}x [∵ 1 + cos 2x = 2 cos^{2}x]

= 2(cos^{2}x + sin^{2}x) – 1

= 2(1) – 1 [∵ cos^{2} θ + sin^{2} θ = 1]

= 2 – 1

= 1

= RHS

∴ LHS = RHS

Hence Proved

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