How do you prove tan(-A)=-tanA?

Nov 17, 2016

see below

Explanation:

$\tan \left(- A\right) = - \tan A$

Use the even and odd property. That is, $\cos \left(- x\right) = \cos x$ and $\sin \left(- x\right) = - \sin x$

Left Side:$= \tan \left(- A\right)$

$= \sin \frac{- A}{\cos} \left(- A\right)$

$= \frac{- \sin A}{\cos} A$

$= - \sin \frac{A}{\cos} A$

$= - \tan A$

$\therefore =$Right Side