Question

Prove that :- sin theta/ 1 - cos theta + tan theta/ 1 + cos theta = sec theta. cosec theta + cot theta​

Answer 1

Answer:

Sinθ/(1 - cosθ)  + Tanθ/(1 + cosθ)  = Secθ.Cosecθ  + Cotθ

Step-by-step explanation:

Sin theta/1-cos theta + tan theta / 1+cos theta = sec theta.cosec theta + cot theta

Sinθ/(1 - cosθ)  + Tanθ/(1 + cosθ)  = Secθ.Cosecθ  + Cotθ

LHS = Sinθ/(1 - cosθ)  + Tanθ/(1 + cosθ)

= (sinθ(1 + cosθ)  + Tanθ(1-Cosθ))/(1 - Cos²θ)

= (sinθ(1 + cosθ) + (Tanθ -  Sinθ)) /Sin²θ

= ( 1 + cosθ  + 1/Cosθ - 1)/Sinθ

= (cosθ  + 1/Cosθ)/Sinθ

= 1/CosθSinθ   + cosθ/Sinθ

= Secθ.Cosecθ + Cotθ

= RHS

QED

Proved