`tan^2 x = 3 tan x` . Solve for x.
To start, subtract both sides by 3tanx.
Factor left side.
`tanx(tanx-3) = 0`
Set each factor to zero and solve for x.
>> `tan x = 0`
`x= tan^(-1)` `(0)`
Note that tangent function is zero at the horizontal axis of unit circle chart. Values of x are:
`x= 0` degrees , `x=180` degrees and `x=360` degrees
>> `tanx - 3=0`
Also, take note that tangent function is positive at the first and third quadrant of unit circle chart. So, values of x are:
`x= 71.6` degrees and `x=251.6` degrees
Since there is no indicated interval for values of x, we should consider the general solution of a tangent function.
The set of all solutions to `tan x = y` is `x = tan^(-1)y + 180k` , where k is any integer.
Hence, the general solutions of the equation `tan^x=3tanx` are:
`x_1= 180k` degrees and `x_2= 71.6 + 180k` degrees.