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Prove the identity `{1-sinx}/cosx=cosx/{1+sinx}` 

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In order to prove the trigonometric identity, we need to start with one side and use known identities to get to the other side:

`LS={1-sinx}/cosx`   multiply by 1+sinx in numerator and denominator

`={1-sinx}/cosx cdot{1+sinx}/{1+sinx}`   expand the numerator

`={1-sin^2x}/{cosx(1+sinx)}`   use identity `1-sin^2x=cos^2x`

`={cos^2x}/{cosx(1+sinx)}`   cancel common factors

`=cosx/{1+sinx}`

`=RS`

The identity has been proved.

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