Question

Show that sin θ + cos θ/ sin θ − cos θ +  sin θ − cos θ/ sin θ + cos θ =  2/sin² θ − cos² θ =  2 /2 sin² θ − 1​

Answer 1

Answer:

•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.