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Prove that: (1+sin2A)/(1-sin2A)=tan^(2...

Prove that:
`(1+sin2A)/(1-sin2A)=tan^(2)(pi/4+A)`

Text Solution

Verified by Experts

LHS=
`=(1+sin2A)/(1-sin2A)=(cos^(2)A+sin^(2)+2sinAcosA)/(cos^(2)A+sin^(2)A-2sinAcosA)`
`=[(cosA+sinA)/(cosA-sinA)]^(2)`
`[(1+tanA)/(1-tanA)]^(2)=[([tanpi/4+tanA]/(1-tanpi/4tanA))^(2)]`
`[tan(pi/4+A)^(2)]=tan^(2)(pi/4+A)=` RHS Hence proved
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