Q15 of 268 Page 5

Prove the following identities :

(sin θ + cos θ)2 + (sin θ – cos θ)2 = 2

Taking LHS = (sin θ + cos θ)2 + (sin θ – cos θ)2

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


= sin2 θ + cos2 θ + 2sin θ cos θ + sin2 θ + cos2 θ – 2sin θ cos θ


= 1 +1 [∵ cos2 θ + sin2 θ = 1]


= 2


=RHS


Hence Proved


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