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Prove that (sintheta-costheta+1)/(sinthe...

Prove that `(sintheta-costheta+1)/(sintheta+costheta-1)=1/(sectheta-tantheta)`, using the identity `sec^2theta=1+tan^2theta`

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L.H.S `(sinθ−cosθ+1)/(sinθ+cosθ−1) = (tanθ+secθ−1)/(tanθ−secθ+1)` ​
`= [(tanθ+secθ)−(sec^2θ−tan^2θ)]/(tanθ−secθ+1)` ​
`=[(tanθ+secθ)−(secθ−tanθ)(secθ+tanθ)]/(tanθ−secθ+1)` ​
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