Question

Prove the following identity:

sinӨ/
1−cos Ө

= cosec Ө + cotӨ.​

Answer 1

Answer:

L.H.S. = 1+cosθ1−cosθ

⇒ L.H.S. = 1+cosθ1−cosθ×1−cosθ1−cosθ

⇒ L.H.S. = 1−cos2θ(1−cosθ)2=sin2θ(1−cosθ)2

⇒ L.H.S. = (sinθ1−cosθ)2=(sinθ1−sinθcosθ)2=(cosecθ−cotθ)2=R.H.S.