Question

Christina is finding the values of x that make the following equation true.

Answer 1

Given

$\tan^2(\frac{x}{2})+2\tan(\frac{x}{2})-5=3\tan(\frac{x}{2})$

Find

Value of x that makes the equation true and what step will she take first

Explanation

to find the value of x , the first step we use

subtract

$3\tan(\frac{x}{2})$

from both sides

on subtraction , we obtain

$\tan^2(\frac{x}{2})-\tan(\frac{x}{2})-5=0$

now ,

$\begin{gathered} \tan(\frac{x}{2})=\frac{-(-1)\pm\sqrt{(-1)^2-4\times1\times(-5)}}{2} \\ \\ \tan(\frac{x}{2})=\frac{1\pm\sqrt{21}}{2} \end{gathered}$

Final Answer

The correct option is C.