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

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Chapter 5, 5.2 - Problem 36 - Precalculus (3rd Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Verify the identity: `csc(-x)/sec(-x)=-cot(x)`

Simplify the left side of the equation using the following even/odd identities:

csc(-x)=-csc(x)  and  sec(-x)=sec(x)

`[-csc(x)]/sec(x)=-cot(x)`

`-csc(x)*1/sec(x)=-cot(x)`

Simplify the left side of the equation using the following reciprocal identities:

csc(x)=1/sin(x)  and 1/sec(x)=cos(x)

`-1/sin(x)*cos(x)=-cot(x)`

`-cos(x)/sin(x)=-cot(x)`

Simplify the left side of the equation using the quotient identity.

`-cot(x)=-cot(x)` 

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