Question

Prove that cot theta+ cosec theta -1/cot theta -cosec theta+1 =1+cos theta/cos theta. ​

Answer 1

Answer:

Prove that

secθ+1

secθ−1

=

1+cosθ

1−cosθ

ANSWER

Solving LHS,

secθ+1

secθ−1

⟹

cosθ

1

+1

cosθ

1

−1

⟹

1+cosθ

1−cosθ

= RHS

Answer 2

Answer:

LHS = (cotθ - cosθ)/(cotθ + cosθ)

putting, cotθ = cosθ/sinθ

= (cosθ/sinθ - cosθ)/(cosθ/sinθ + cosθ)

= {cosθ(1/sinθ - 1)}/{cosθ(1/sinθ - 1)}

= (1/sinθ - 1)/(1/sinθ - 1)

we know, 1/sinθ = cosecθ

= (cosecθ - 1)/(cosecθ + 1) = RHS

hence proved.

hope this helps you