`sec(x) - cos(x) = sin(x)tan(x)` Verfiy the identity.

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Chapter 5, 5.2 - Problem 25 - Precalculus (3rd Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Verify the identity: `sec(x)-cos(x)=sin(x)tan(x)`

The reciprocal of sec(x)=1/cos(x).

`sec(x)-cos(x)=sin(x)tan(x)`

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

`[1-cos^2(x)]/cos(x)=sin(x)tan(x)`

Use the pythagorean identity `sin^2(x)+cos^2(x)=1`

If `sin^2(x)`    is isolated the pythagorean identity would be `sin^2(x)=1-cos^2(x)`

``

`[sin^2(x)]/cos(x)=sin(x)tan(x)`

`sin(x)sin(x)/cos(x)=sin(x)tan(x)`

`sin(x)tan(x)=sin(x)tan(x)`

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