Use the cofunction identities to find an angle that makes the statement true.
-$$\frac { 1 + \tan ^ { 2 } x } { \sec x }$$
A) 1
B) $- \sec x$
C) $\csc x$
D) $\sec x$

Question

Quizplus · Accepted Answer

The cofunction identity for secant is $\sec x = \csc (90^\circ - x)$. Substituting this into the expression gives:$$\frac { 1 + \tan ^ { 2 } x } { \sec x } = \frac { 1 + \tan ^ { 2 } x } { \csc (90^\circ - x) }$$Using the Pythagorean identity $\tan ^ { 2 } x + 1 = \sec ^ { 2 } x$, this simplifies to:$$\frac { 1 + \tan ^ { 2 } x } { \sec x } = \frac { \sec ^ { 2 } x } { \csc (90^\circ - x) }$$$$\frac { 1 + \tan ^ { 2 } x } { \sec x } = \sec (90^\circ - x)$$Therefore, the angle that makes the statement true is $90^\circ - x$, which is choice D.

Use the Cofunction Identities to Find an Angle That Makes 1+tan⁡2xsec⁡x\frac { 1 + \tan ^ { 2 } x } { \sec x }secx1+tan2x​

Use the Cofunction Identities to Find an Angle That Makes $\frac { 1 + \tan ^ { 2 } x } { \sec x }$