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(1+cosx)/(1-cosx)=tan^2x/(secx-1)^2...

`(1+cosx)/(1-cosx)=tan^2x/(secx-1)^2`

Text Solution

Verified by Experts

LHS=`(1+cosx)/(1-cosx)=((1+cosx)(1-cosx))/(1-cosx)^2`
`=(1-cos^2x)/(1-1/secx)^2=sin^2x/((secx-1)^2/sec^2x)`
`=(sin^2x*sec^2x)/(secx-1)^2`
`=((sin^2x)/(cosx))/(secx-1)^2`
`=tan^2x/(secx-1)^2`
RHS.
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