Question

Prove that whole root (1+cos theta)/(1-cos theta)+whole root (1-cos theta)/(1+cos theta)=2 cosec theta

Answer 1

√{(1+cosθ)/(1-cosθ)}+√{(1-cosθ)/(1+cosθ)}
=(√1+cosθ×√1+cosθ+√1-cosθ×√1-cosθ)/(√1-cosθ×√1+cosθ)
={√(1+cosθ)²+√(1-cosθ)²}/√(1-cos²θ)
=(1+cosθ+1-cosθ)/√sin²θ
=2/sinθ
=2cosecθ (Proved)

Answer 2

I hope it helps you

In the picture rationalization is done and then add it hence fundamental identity is applied