Question

If cos theta + sin theta = 1 then prove that cos theta - sin theta = ±1​

Answer 1

Step-by-step explanation:

Given

cosθ+sinθ=1

(cosθ+sinθ)

2

=1

2

cos

2

θ+sin

2

θ+2sinθcosθ=1

1+2sinθcosθ=1

2sinθcosθ=0

sinθcosθ=0

Now (cosθ−sinθ)

2

=(cosθ+sinθ)

2

−4sinθcosθ

=1

2

−4×0

=1

(cosθ−sinθ)

2

=1

cosθ−sinθ=±1

∴ Hence proved.