Chapter 13.1, Problem 46HP

To determine

To Prove: The expression $\text{tan(}-\text{a)}=-\tan a$

Explanation of Solution

Given:

The expression is $\text{tan(}-\text{a)}=-\tan a$

Calculation :

  $\begin{array}{l}\text{In}\text{ΔOAB:-}\\ \tan a=\frac{q}{p}\cdot \cdot \cdot \cdot (1)\\ \text{In}\text{ΔOAC:-}\\ \tan (-a)=\frac{-q}{p}\\ \tan (-a)=-\left(\frac{q}{p}\right)\cdot \cdot \cdot \cdot (2)\\ \text{From}\text{equation}\text{(1)}\text{:-}\\ \tan (-a)=-\tan a\end{array}$

  

Hence proved.