Solve the equation for solutions in the interval [0, 2 $$[ 0,2 \pi )$$
-$$\sec \frac { x } { 2 } = \cos \frac { x } { 2 }$$
A) $\left\{ 0 , \frac { \pi } { 4 } , \pi , \frac { 5 \pi } { 3 } \right\}$
B) $\{ 0 \}$
C) $\left\{ \frac { \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$
D) $\left\{ \frac { \pi } { 12 } , \frac { \pi } { 6 } , \frac { 2 \pi } { 3 } , \frac { 7 \pi } { 12 } , \frac { 7 \pi } { 6 } , \frac { 13 \pi } { 12 } , \frac { 5 \pi } { 3 } \right\}$

Question

Quizplus · Accepted Answer

The equation $\sec \frac { x } { 2 } = \cos \frac { x } { 2 }$ simplifies to $1 = \cos^2 \frac { x } { 2 }$ because $\sec \theta = \frac{1}{\cos \theta}$. This equation holds true when $\cos \frac { x } { 2 } = 1$, which occurs at $x = 0$ within the given interval $[0, 2\pi)$.

Solve the Equation for Solutions in the Interval [0, 2 [0,2π)[ 0,2 \pi )[0,2π)

Solve the Equation for Solutions in the Interval [0, 2 $[ 0,2 \pi )$