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How to prove (cosx)/(1-sinx) = (1+sinx)/cosx  

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farajallah | eNotes Newbie

Posted May 5, 2013 at 11:05 AM via web

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How to prove

(cosx)/(1-sinx) = (1+sinx)/cosx

 

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted May 5, 2013 at 11:22 AM (Answer #1)

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We know

`cos^2(x)+sin^2(x)=1`

`LHS=cos(x)/(1-sin(x))`

`={cos(x)(1+sin(x))}/{(1-sin(x))(1+sin(x))}`

`={cos(x)(1+sin(x))}/{1-sin^2(x)}`

`={cos(x) (1+sin(x))}/{cos^2(x)}`

`=(1+sin(x))/cos(x)`

`=RHS`

``

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