`(cot^2(t))/csc(t) = (1 - sin^2(t))/sin(t)` Verfiy the identity.

Textbook Question

Chapter 5, 5.2 - Problem 19 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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`cot(t) = cos(t)/sin(t),` `csc(t) = 1/sin(t).`

So `(cot^2(t))/csc(t) = (cos^2(t))/(sin^2(t))*(1/(1/sin(t))) =(cos^2(t))/(sin^2(t))*sin(t) = (cos^2(t))/sin(t),`

which is the same as the right part because `1-sin^2(t) = cos^2(t).`

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