Answer :

To Prove: (sin x – cos x)2 = 1 – sin 2x

Taking LHS,


= (sin x – cos x)2


Using,


(a b)2 = (a2 + b2 – 2ab)


= sin2x + cos2x – 2sinx cosx


= (sin2x + cos2x) – 2sinx cosx


= 1 – 2sinx cosx [ cos2 θ + sin2 θ = 1]


= 1 – sin2x [ sin 2x = 2 sinx cosx]


= RHS


LHS = RHS


Hence Proved


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