If x =(2 sin Θ)/(1+ cos????Θ + sinΘ), then (1 - cos Θ + sinΘ)/(1 + sinΘ ) is equal to

(a) 1+x (b) 1-x (c) x (d) 1/x

Pls explain.

given x = (2sinθ)/( 1+sinθ+cosθ)

multiplying the numerator and the denominator by (1+sinθ-cosθ)

x = (2sinθ)(1+sinθ-cosθ)/((1+sinθ)²-(cosθ)²)

on simplifying you will get same the desired as (1-cosθ+sinθ)/(1+sinθ) which is x.