# If cos θ +sin θ=1, prove that cos θ – sin θ = ± 1

Using the formula,

(a+b)2 + (a – b)2 = 2(a2+b2)

(cos θ +sin θ)2 + (cos θ – sin θ)2 = 2(cos2θ + sin2 θ)

1 + (cos θ – sin θ)2 = 2(1)

(cos θ – sin θ)2 = 2 –1

(cos θ – sin θ)2 = 1

(cos θ – sin θ) =√1

(cos θ – sin θ) = ±1

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