Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
-$$\frac { 1 + \tan ^ { 2 } x } { \sec x }$$
A) 1
B) $- \sec x$
C) $\sec x$
D) $\csc x$

Question

Quizplus · Accepted Answer

The given expression can be simplified using trigonometric identities. Recall that $\tan^2x + 1 = \sec^2x$ and $\sec x = \frac{1}{\cos x}$. Substituting these into the expression gives:$$\frac{1 + \tan^2x}{\sec x} = \frac{\sec^2x}{\sec x} = \sec x$$Therefore, the expression simplifies to $\sec x$.

Write the Expression in Terms of Sine and Cosine, and Simplify