Q15 of 268 Page 5

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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