Prove that 1-cos2A+sin2A/1+cos2A+sin2A=tanA

Steps to prove 1-cos2A+sin2A/1+cos2A+sin2A=tanA

Take L.H.S

=1-cos2A+sin2A/1+cos2A+sin2A

We Know that

[1-cos2A=2sin^2A]

[1+cos2A=2cos^2A]

[sin2A=2sinA.cosA]

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

=2sinA(sinA+cosA)/2cosA(cosA+sinA)

=2sinA/2cosA=tanA

=R.H.S

Hence 1-cos2A+sin2A/1+cos2A+sin2A=tanA is proved

Detail Information:-

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