Solve the equation in the interval $[ 0,2 \pi )$ . $\tan x \cos x - \cos x = 0$
A) $x = \frac { \pi } { 4 }$, $x = - \frac { \pi } { 4 }$, $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 2 }$

B) $x = 0$, $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 4 }$, $x = \frac { 5 \pi } { 4 }$

C) $x = 0$, $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 4 }$

D) $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 4 }$, $x = \frac { 5 \pi } { 4 }$

E) none of these

Question

Solve the equation in the interval $[ 0,2 \pi )$ . $\tan x \cos x - \cos x = 0$
A) $x = \frac { \pi } { 4 }$, $x = - \frac { \pi } { 4 }$, $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 2 }$

B) $x = 0$, $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 4 }$, $x = \frac { 5 \pi } { 4 }$

C) $x = 0$, $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 4 }$

D) $x = \frac { \pi } { 2 }$, $x = \frac { 3 \pi } { 4 }$, $x = \frac { 5 \pi } { 4 }$

E) none of these

Quizplus · Accepted Answer

The given equation can be simplified to $\tan x \cos x - \cos x = \cos x (\tan x - 1) = 0$. This implies $\cos x = 0$ or $\tan x = 1$. Solving for $x$ in the interval $[0, 2\pi)$, $\cos x = 0$ gives $x = \frac{\pi}{2}, \frac{3\pi}{2}$, and $\tan x = 1$ gives $x = \frac{\pi}{4}, \frac{5\pi}{4}$. None of the provided options exactly match these solutions.

Solve the Equation in the Interval [0,2π)[ 0,2 \pi )[0,2π) tan⁡xcos⁡x−cos⁡x=0\tan x \cos x - \cos x = 0tanxcosx−cosx=0

Solve the Equation in the Interval $[ 0,2 \pi )$ $\tan x \cos x - \cos x = 0$