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

Textbook Question

Chapter 5, 5.2 - Problem 44 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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First, `sec(y) = 1/cos(y)` and `cot(y) = cos(y)/sin(y).`

Second, `cos(pi/2-y) = sin(y)` and  `sin(pi/2-y) = cos(y).`

Therefore

`sec^2(y) - cot^2(pi/2-y) = 1/(cos^2(y)) - (sin^2(y))/(cos^2(y)) =`

`(1-sin^2(y))/(cos^2(y)) = (cos^2(y))/(cos^2(y)) = 1,`

`QED`

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