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Check whether the equation (tanphi+sinph...

Check whether the equation `(tanphi+sinphi)/(tanphi-sinphi)=(secphi+1)/(secphi-1)` is an identity or not ?

Text Solution

Verified by Experts

L.H.S.`=(tanphi+sinphi)/(tanphi-sinphi)=((sinphi)/(cosphi)+sinphi)/((sinphi)/(cosphi)-sinphi)`
`=(sinphisec+sinphi)/(sinphisecphi-sinphi)=(sinphi(secphi+1))/(sinphi(secphi-1))=(secphi+1)/(secphi-1)=R.H.S`.
`:'` " " L.H.S.=R.H.S.
And this equation is true for all values of `phi`.
`:.` Given equation is an identy.
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