Question

If CosØ + SinØ = 1 then prove that CosØ - SinØ = $\pm1$

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Answer 1

Given :- CosØ + SinØ = 1 --------(1)

Let, CosØ - SinØ = x ----------(2)

Squaring and both both equations :-

= (CosØ+SinØ)^2 + (CosØ-SinØ)^2 = 1^2 + x^2

= Cos^2Ø + Sin^2Ø + 2 CosØ.SinØ + Cos^2Ø + Sin^2Ø - 2 CosØ.SinØ = 1 + x^2

= 1 + 1 = 1 + x^2

= x = $\sqrt{1}$

= x = $\pm{1}$

= CosØ-SinØ = $\pm{1}$