#LHS=(1+cos theta +sin theta)/(1+ cos theta-sin theta)#
#=(costheta(1+cos theta +sin theta))/(costheta(1+ cos theta-sin theta))#
#=(costheta(1+ sintheta)+cos^2 theta )/(costheta(1+ cos theta-sin theta))#
#=(costheta(1+ sintheta)+(1-sin^2 theta ))/(costheta(1+ cos theta-sin theta))#
#=((1+ sintheta)(costheta+1-sintheta ))/(costheta(1+ cos theta-sin theta))#
#=((1+ sintheta)cancel((1+costheta-sintheta )))/(costhetacancel((1+ cos theta-sin theta)))#
#=(1+sintheta)/costheta=RHS#