`tan(pi/2 - theta) tan(theta) = 1` Verfiy the identity.

Textbook Question

Chapter 5, 5.2 - Problem 33 - Precalculus (3rd Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

By definition, tan(t)=sin(t)/cos(t).

Also, `sin(pi/2-t)=cos(t)` and `cos(pi/2-t)=sin(t).`

Therefore `tan(pi/2-t)=cos(t)/sin(t)` and

`tan(pi/2-t)*tan(t)=1,` QED.

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Seema Adiga | High School Teacher | (Level 2) Adjunct Educator

Posted on

`tan(pi/2-theta) = cot theta`

`cot theta * tan theta = 1/ tan theta * tan theta `

`= 1`

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