Question

Solve the equation for x in the interval [0,2π). Use exact solutions where possible and give approximate solutions correct to four decimal places.

Answer 1

From the problem, we have an equation of :

$2\tan ^2x+3\tan x+1=0$

Factor completely :

$(2\tan x+1)(\tan x+1)=0$

Equate both factors to 0 :

$\begin{gathered} 2\tan x+1=0 \\ 2\tan x=-1 \\ \tan x=-\frac{1}{2} \\ x=\arctan (-\frac{1}{2}) \\ x=-26.565\ldots \end{gathered}$$\begin{gathered} \tan x+1=0 \\ \tan x=-1 \\ x=\arctan (-1) \\ x=\frac{1}{4}\pi,\frac{3}{4}\pi \end{gathered}$

The only exact values of x are π/4 and 3π/4

The answers are π/4 and 3π/4