Chapter 14.3, Problem 24PPS

To determine

To Calculate:The value of $\tan {165}^{\circ }$ .

Answer to Problem 24PPS

  $\sqrt{3}-2.$

Explanation of Solution

Given information:

We know that, the given expression is $\tan {165}^{\circ }$ .

Formula used:

  $\tan ({180}^{\circ }-\text{θ})=-\tan \text{θ},\tan {15}^{\circ }=2-\sqrt{3}$ .

Calculation:

  $\begin{array}{l}\tan {165}^{\circ }=\tan ({180}^{\circ }-{15}^{\circ })\text{.}\\ =-\tan {15}^{\circ }\\ \text{=}-(2-\sqrt{3})\\ =\sqrt{3}-2\end{array}$