Question

prove that √1+Cotθ /1-Cotθ=Cosecθ+Cotθ​

Answer 1

Step-by-step explanation:

LHS - Multiplying both Numerator & Denominator by 1−cosθ

(1+cosθ)(1−cosθ)(1−cosθ)(1−cosθ)

⇒1−cos2θ(1−cosθ)2

                         {∵sin2x+cos2x=1}

⇒sin2θ(1−cosθ)2⇒(sinθ)∣1−cosθ∣

taking + values only positive.

⇒sinθ1−cosθ

⇒sinθ1−sinθcosθ

⇒cosecθ−cotθ

  = RHS