Question

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

Answer 1

Given

`\tan^2((x)/(2))+2\tan((x)/(2))-5=3\tan((x)/(2))`

Find

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

Step-by-step explanation

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

subtract

`3\tan((x)/(2))`

from both sides

on subtraction , we obtain

`\tan^2((x)/(2))-\tan((x)/(2))-5=0`

now ,

`\begin{gathered} \tan((x)/(2))=(-(-1)\pm√((-1)^2-4*1*(-5)))/(2) \\ \\ \tan((x)/(2))=(1\pm√(21))/(2) \end{gathered}`

Final Answer

The correct option is C.