How do you prove #tan theta cot theta=1#?

2 Answers
Alan P. · Kevin B.
Jun 8, 2015

By definition #cot(theta) = 1/(tan(theta))#

Explanation:

#tan(theta) * cot(theta)#

#color(white)("XXXX")##= tan(theta) * 1/tan(theta)#

#color(white)("XXXX")##= cancel(tan(theta))* 1/cancel(tan(theta))#

#color(white)("XXXX")##=1#

Arunraju Naspuri · Stefan V.
Jun 9, 2015

We can prove it by right angle triangle.

Explanation:

![http://www.mathportal.org/calculators/plane-geometry-calculators/http://right-triangle-calculator.php](https://useruploads.socratic.org/enqJSZMS6yK8CLpGBlRq_triangleRightAngle.gif)

#tan( α )=a/b#

#cot(α )=b/a#;

#LHS=tan(alpha)xxcot(alpha)#

#=a/bxxb/a#

#=(cancela)/cancel(b)xx(cancel(b)/cancel(a))#

=1

=RHS

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