`sec(x)(csc(x) - 2sin(x)) = cot(x) - tan(x)` Verify the identity.

Textbook Question

Chapter 5, 5.2 - Problem 26 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Transform the left side:

`sec(x)*(csc(x)-2sin(x))=(1/cos(x))*((1-2sin^2(x))/sin(x)=(cos^2(x)-sin^2(x))/(cos(x)*sin(x)).`

The right side is

`cos(x)/sin(x)-sin(x)/cos(x)=(cos^2(x)-sin^2(x))/(sin(x)*cos(x)),`

which is the same.

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