`cot(x)/sec(x) = csc(x) - sin(x)` Verfiy the identity.

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Chapter 5, 5.2 - Problem 23 - Precalculus (3rd Edition, Ron Larson).
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embizze | High School Teacher | (Level 1) Educator Emeritus

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Verify cot(x)/sec(x)=csc(x)-sin(x):

Working from the left side, we show that it is equivalent to the right side:

cot(x)/sec(x)

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

`=(cos^2(x))/(sin(x))`

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

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

=csc(x)-sin(x) as required.

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