Question

prove RHS= LHS
urgent

Answer 1

LHS:

We need to take the LCM then we get,

cosec θ( cosec θ+1) + cosecθ(cosecθ-1)/ (cosecθ+1) (cosecθ-1)

then if we further simplify it we get,

cosec²θ+ cosecθ + cosec²θ-cosecθ/cosec²θ-1 ( + cosecθ and - cosecθ gets cancelled)

Then we get,

2cosec²θ/cosec²θ-1

as we know

cosecθ=1/sinθ

2/sin²θ / 1/sin²θ-1 ← LCM

2/ sin²θ / 1-sin²θ/sinθ  ( Sin²θ from both denominators)

then,

2/ 1- sin²θ  ( identity sin²θ +cos²θ =1 ⇒ cos²θ =1-sin²θ )

2/ cos²θ

and we know that

1/cosθ =secθ

Therefore,

2/ cos²θ  = 2sec²θ

RHS:

2sec²θ

Therefore,

LHS = RHS