Solve the equation for exact solutions over the interval [0, 2 $$[ 0,2 \pi )$$
-$$\sec ^ { 2 } x - 2 = \tan ^ { 2 } x$$
A) $\left\{ \frac { \pi } { 3 } \right\}$
B) $\left\{ \frac { \pi } { 4 } \right\}$
C) $\varnothing$
D) $\left\{ \frac { \pi } { 6 } \right\}$

Question

Quizplus · Accepted Answer

Using the trigonometric identity $\sec^2x = 1 + \tan^2x$, the equation becomes $1 + \tan^2x - 2 = \tan^2x$, which simplifies to $-1 = 0$, an impossibility. Therefore, there are no solutions.

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

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