Question

sinθ÷1- cosθ + tanθ÷1+cosθ = secθ.cosecθ + cotθ

Answer 1

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