The solution set of the equation sec x = csc x on $[ 0,2 \pi ]$ is

A) $\left\{ \frac { \pi } { 4 } \right\}$
B) $\left\{ \frac { 5 \pi } { 4 } \right\}$
C) $\left\{ \frac { 7 \pi } { 4 } \right\}$
D) $\left\{ \frac { \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$
E) $\varnothing$

Question

The solution set of the equation sec x = csc x on $[ 0,2 \pi ]$ is

A) $\left\{ \frac { \pi } { 4 } \right\}$
B) $\left\{ \frac { 5 \pi } { 4 } \right\}$
C) $\left\{ \frac { 7 \pi } { 4 } \right\}$
D) $\left\{ \frac { \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$
E) $\varnothing$

Quizplus · Accepted Answer

Sec(x) = csc(x) implies 1/cos(x) = 1/sin(x), which simplifies to sin(x) = cos(x). This equation holds true at x = π/4 and x = 5π/4 within the given interval [0, 2π].

The Solution Set of the Equation Sec X = Csc [0,2π][ 0,2 \pi ][0,2π]

The Solution Set of the Equation Sec X = Csc $[ 0,2 \pi ]$