Question

if cos A - sin A= 1, then prove that cos A+ sinA=1 or -1​

Answer 1

cosθ+sinθ=1

(cosθ+sinθ) ^2 =1^2

cos 2θ+sin 2θ+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.