The expression E=1+cosθ+sinθ1+cosθ−sinθ can be simplified to
(1+sinθ)/cosθ
We multiply the numerator and denominator of E by cos θ -
E=cosθ(1+cosθ+sinθ)cosθ(1+cosθ−sinθ)=cosθ+sinθ.cosθ+cos2θcosθ(1+cosθ−sinθ)=cosθ(1+sinθ)+(1−sin2θ)cosθ(1+cosθ−sinθ)=(1+sinθ)(cosθ+1−sinθ)cosθ(1+cosθ−sinθ)=1+sinθcosθ