Prove that √(1-sinA)/(1+sinA)=tan(π/4+A/2)

Steps to prove √(1-sinA)/(1+sinA)=tan(π/4+A/2)

Take L.H.S

=√(1-sinA)/(1+sinA)

=√(cos^2A/2+sin^2A/2+2sinAcosA/2)/(cos^2A/2+sin^2A/2+2sinAcosA/2)

={(cosA/2+sinA/2)/cosA/2}/{(cosA/2-sinA/2)/cosA/2}

=(1+tanA/2)/(1-tanA/2)

=(tanπ/4+tanA/2)/(1-tanπ/4.tanA/2)  [tanπ/4=1]

=tan(π/4+A/2)

=R.H.S

Hence √(1-sinA)/(1+sinA)=tan(π/4+A/2) is Proved

Detail Information:-

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