# Derivative of Tan Demonstration

**Tan**

Demonstration of derivative of Tan

This demonstration is a simple application of the quotient rule to the definition of Tan.

{$$ \large \begin{align} {d \over {d\theta}} \tan\theta &= {d \over {d\theta}} \left( {{\sin\theta} \over {\cos\theta}} \right) \cr &= {{ \cos\theta{d \over {d\theta}}\sin\theta -\sin\theta {d \over {d\theta}}\cos\theta} \over {\cos^2\theta}} \tag{quotient rule} \cr &= {{\cos^2\theta} \over {\cos^2\theta}} + {{\sin^2\theta} \over {\cos^2\theta}} \cr &= 1 + \tan^2\theta \end{align} $$}

{$$ \Large \therefore {d \over {d\theta}} \tan\theta = \sec^2\theta \tag{Pythagorean identity} $$}

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** Categories:** Derivative Demonstrations

** Tags** XxxTan XxxSec XxxDerivative XxxDemonstration XxxQuotient Rule

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