Question

if cos theta + sin theta =1,prove that cos theta-sin theta=+-1

Answer 1

Using the formula

(a+b)2+(a−b)2=2(a2+b2)

(cosθ+sinθ)2+(cosθ−sinθ)2=2(sin2θ+cos2θ)

⇒12+(cosθ−sinθ)2=2×1

⇒(cosθ−sinθ)2=2−1=1

⇒cosθ−sinθ=±1


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Answer 2

The solution is provided in the attachment .
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