Q. 15 G4.0( 3 Votes )

# Prove the following identities :cos4 A + sin4 A + 2 sin2 A. cos2 A = 1

Taking LHS = cos4 A + sin4 A + 2 sin2 A cos2 A

Using the identity,(a + b)2 = (a2 + b2 + 2ab)

Here, a = cos2 A and b = sin2 A

= ( cos2 A + sin2 A) [ cos2 θ + sin2 θ = 1]

= 1

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