Question #e16fe

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Answer 1 · 2017-09-19T03:01:17

#LHS=(sin⁡θ-cos⁡θ+1)/(sin⁡θ+cos⁡θ-1)#

#=(costheta(sin⁡θ-cos⁡θ+1))/(costheta(sin⁡θ+cos⁡θ-1))#

#=(costhetasin⁡θ-cos⁡^2θ+costheta)/(costheta(sin⁡θ+cos⁡θ-1))#

#=(costhetasin⁡θ+costheta-(1-sin⁡^2θ))/(costheta(sin⁡θ+cos⁡θ-1))#
#=(costheta(sin⁡θ+1)-(1-sin⁡θ)(1+sintheta))/(costheta(sin⁡θ+cos⁡θ-1))#

#=((sin⁡θ+1)(costheta-1+sin⁡θ))/(costheta(sin⁡θ+cos⁡θ-1))#

# =(sin⁡θ+1)/(cos⁡θ)=RHS#

Proved