Q. 15 D5.0( 2 Votes )

# Prove the following identities :(sin θ – cos θ)2 = 1 – 2 sinθ . cos θ

Taking LHS = (sin θ – cos θ)2

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

= sin2 θ + cos2 θ – 2sin θ cos θ

= 1 – 2sin θ cos θ [ cos2 θ + sin2 θ = 1]

=RHS

Hence Proved

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