Q. 12

# Prove that</p

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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