`cot^2(y)(sec^2(y) - 1) = 1` Verfiy the identity.

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Chapter 5, 5.2 - Problem 11 - Precalculus (3rd Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Verify the identity: `cot^2(y)[sec^2(y)-1]=1`

Use the pythagorean identity `1+tan^2(y)=sec^2(y).`

If  `tan^2(y)`  is isolated the identity would be `tan^2(y)=sec^2(y)-1.`

`cot^2(y)[sec^2(y)-1]=1`

`cot^2(y)[tan^2(y)]=1`

Because tan(y) and cot(y) are reciprocals their product is equal to 1.

`1=1` 

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