Question

Answer please. Class 10th ​

Answer 1

Answer:

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

Let us start with 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

Hence Proved