Chapter 14.4, Problem 22PPS

To determine

To Find:The value of $\tan \left(\frac{5\pi }{12}\right)$

Answer to Problem 22PPS

  $\frac{\sqrt{3}+1}{\sqrt{3}-1}$

Explanation of Solution

Given:- We know that the given expression is $\tan \left(\frac{5\pi }{12}\right)$

Calculation:

  $\begin{array}{l}\Rightarrow \tan \left(\frac{5\pi }{12}\right)\\ \Rightarrow \tan \left(\pi -\frac{7\pi }{12}\right)\\ \Rightarrow -\tan \left(\frac{7\pi }{12}\right)\\ \Rightarrow -\tan \left(\frac{\pi }{4}+\frac{\pi }{3}\right)\\ \Rightarrow -\left(\frac{\tan \frac{\pi }{4}+\tan \frac{\pi }{3}}{1-\tan \frac{\pi }{4}\tan \frac{\pi }{3}}\right)\\ \Rightarrow -\left(\frac{1+\sqrt{3}}{1-\sqrt{3}}\right)\\ \Rightarrow \frac{\sqrt{3}+1}{\sqrt{3}-1}\end{array}$