Question

If cosθ−sinθ=2–√sinθ , then cosθ+sinθ=​

Answer 1

Answer:

Correct option is

A

2

cosθ

Given,

cosθ−sinθ=

2

sinθ

Squaring, we get

cos

2

θ+sin

2

θ−2sinθcosθ=2sin

2

θ

or 1−2sinθcosθ=2(1−cos

2

θ)

or 1+2sinθcosθ=2cos

2

θ

or sin

2

θ+cos

2

θ+2sinθcosθ=2cos

2

θ

or (sinθ+cosθ)

2

=2cos

2

θ

∴sinθ+cosθ=

2

cosθ