Question

2tan^2 x - tank-6=0 solve for 0°< × < 360°

Answer 1

Given the equation,

`2tan^2x\text{ - tan x - 6 =0}`

We want to get the value of x within 0 degree and 360 degrees, that can satisfy the equation.

Next, we need to factorise,

But before then,

Let y = tan x.

so that 2y^2 - y - 6 =0,

Factorising we have :

2y ( y-3 ) +2 (y-3) = 0,

( y-3) ( 2y +2 ) = 0

Then y=3 or y = -1

If y= 3, then

`\begin{gathered} x\text{ = }\tan ^(-1)(\text{ 3)} \\ x\text{ =71.56 degre}es \\ \\ \text{If y }=\text{ -1,} \\ x\text{ = }\tan ^(-1)\text{ ( -1)} \\ x\text{ = 135 degr}ees\text{ or 315 degr}ees \end{gathered}`