Prove that (1+sinA-cosA)/(1+sinA+cosA)=tan(A/2)

Steps to prove (1+sinA-cosA)/(1+sinA+cosA)=tan(A/2)

L.H.S

=(1+sinA-cosA)/(1+sinA+cosA)

=(1-cosA+sinA)/(1+cosA+sinA)

={2sin^2(A/2)+2sin(A/2).coso(A/2)}/{2cos^2(A/2)+2sin(A/2).coso(A/2)}

=2sin(A/2){sin(A/2)+cos(A/2)}/2cos(A/2){sin(A/2)+cos(A/2)}

=sin(A/2)/cos(A/2)=tan(A/2)

=R.H.S

Hence (1+sinA-cosA)/(1+sinA+cosA)=tan(A/2) is proved.

Detail Information:-

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