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