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Question
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
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Solution
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
= L.H.S.
= `(sec"A"-1)/(sec"A"+1)`
= `(1/cosA-1)/(1/cosA+1)`
=`(1-cosA)/(1+cosA)`
Multiplied by 1 + cosA
=`(1-cos^2A)/(1+cosA)^2`
=`(sin^2A)/(1+cosA)^2`
=`((sinA)/(1+cosA))^2`
= R.H.S
Hence Proved.
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