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Prove the identity: `(sin^2x)/(1-cosx)=(secx+1)/secx`

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math30fails | Student, Undergraduate | (Level 1) Honors

Posted April 5, 2012 at 3:08 AM via web

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Prove the identity: `(sin^2x)/(1-cosx)=(secx+1)/secx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 5, 2012 at 3:15 AM (Answer #1)

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The identity to prove is `(sin^2 x)/(1-cos x)= (sec x+1)/sec x`

`(sin^2x)/(1-cos x)`

=> `(1 - cos^2x)/(1 - cos x)`

=> `((1 + cos x)(1 - cos x))/(1 - cos x)`

=> `(1 + cos x)`

=> `(1 + 1/sec x)`

=> `(sec x + 1)/sec x`

This proves that `(sin^2x)/(1-cosx)=(secx+1)/secx`

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