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Prove the identity (tantheta+sectheta-1)...

Prove the identity `(tantheta+sectheta-1)/(tantheta-sectheta+1)=(1+sintheta)/(costheta)`

Text Solution

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L.H.S `=\frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}`
We can write, `\sec ^{2} \theta-\tan ^{2} \theta=1`
`=\frac{\tan \theta+\sec \theta-(\sec ^{2} \theta-\tan ^{2} \theta)}{\tan \theta-\sec \theta+1}`

`=\frac{\tan \theta+\sec \theta-(\sec \theta-\tan \theta)(\sec \theta+\tan \theta)}{\tan \theta-\sec \theta+1}` ...
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