simplify.
sec x - sec x sin²x
use algebra and the fundamental trigonometric identities.
your answer should be a number or use a single trigonometric function.

Question

Accepted Answer

# Explanation:
## Step1: Factor out $\sec x$
$$
\begin{align*}
\sec x-\sec x\sin^{2}x&=\sec x(1 - \sin^{2}x)
\end{align*}
$$
## Step2: Use the Pythagorean identity $\cos^{2}x=1-\sin^{2}x$
$$
\begin{align*}
\sec x(1 - \sin^{2}x)&=\sec x\cdot\cos^{2}x
\end{align*}
$$
## Step3: Use the reciprocal identity $\sec x=\frac{1}{\cos x}$
$$
\begin{align*}
\sec x\cdot\cos^{2}x&=\frac{1}{\cos x}\cdot\cos^{2}x\
&=\cos x
\end{align*}
$$

# Answer:
$\cos x$

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Question

Explanation:

Step1: Factor out \(\sec x\)

Step2: Use the Pythagorean identity \(\cos^{2}x=1-\sin^{2}x\)

Step3: Use the reciprocal identity \(\sec x=\frac{1}{\cos x}\)

Answer: