Verified answer

Starting from the right

(1 - Cosθ) / Sinθ = 1/Sinθ - Cosθ/Sinθ = Cosecθ - Cotθ

Multiply Numerator and Denominator by Cosecθ + Cotθ

[(Cosecθ - Cotθ)(Cosecθ + Cotθ)] / (Cosecθ + Cotθ)

(Cosec²θ - Cot²θ)/(Cosecθ + Cotθ)

= 1/(Cosecθ + Cotθ)

(Since Cosec²θ - Cot²θ = 1)

caution : put parenthesis...

hope it' ll help !!