Question

29. Show that
sin theta /cosec theta -1 + cos theta /1+sec theta= sin theta cos theta /(sin theta - cos theta)​

Answer 1

Step-by-step explanation:

Given:- sinθ+cosθ=

2

cosθ

To prove:- cosθ+sinθ=

2

sinθ

Proof:-

sinθ+cosθ=

2

cosθ

Squaring both sides, we get

sin

2

θ+cos

2

θ+2sinθcosθ=2cos

2

θ

⇒sin

2

θ−cos

2

θ+2sinθcosθ=0

Subtracting 2sin

2

θ both sides, we have

−sin

2

θ−cos

2

θ+2sinθcosθ=−2sin

2

θ

sin

2

θ+cos

2

θ−2sinθcosθ=2sin

2

θ

(cosθ−sinθ)

2

=2sin

2

θ

⇒cosθ−sinθ=

2

sinθ

Hence proved.