Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers
in radians to four decimal places and approximate answers in degrees to the nearest tenth.
-$\tan x ( \tan x - 2 ) = 6$
A) $\{ 1.3031 + \mathrm { n } \pi , 2.1168 + \mathrm { n } \pi \}$
B) $\{ 1.2490 + \mathrm { n } \pi , 2.3562 + \mathrm { n } \pi \}$
C) $\{ 1.2490 + \mathrm { n } \pi , 5 + \mathrm { n } \pi \}$
D) $\{ 1.3031 + \mathrm { n } \pi , 5.2584 + \mathrm { n } \pi \}$

Question

Quizplus · Accepted Answer

The equation $\tan x ( \tan x - 2 ) = 6$ simplifies to a quadratic equation in terms of $\tan x$, which is $\tan^2 x - 2\tan x - 6 = 0$. Solving this quadratic equation gives two solutions for $\tan x$, which then can be used to find the values of $x$ in radians. The correct solutions in radians are $1.3031 + n\pi$ and $2.1168 + n\pi$, which correspond to the periodic nature of the tangent function, where $n$ is any integer.

Solve the Equation (X in Radians and in Degrees) for All