Simplify sec(theta)^2*cos(theta)^2

$\sec^{2} (θ) \cdot \cos^{2} (θ)$

Step 1

Rewrite $\sec (θ)$ in terms of sines and cosines.

${(\frac{1}{\cos (θ)})}^{2} \cdot \cos^{2} (θ)$

Step 2

Simplify the expression.

Apply the product rule to $\frac{1}{\cos (θ)}$ .

$\frac{1^{2}}{\cos^{2} (θ)} \cdot \cos^{2} (θ)$

One to any power is one.

$\frac{1}{\cos^{2} (θ)} \cdot \cos^{2} (θ)$

$\frac{1}{\cos^{2} (θ)} \cdot \cos^{2} (θ)$

Step 3

Cancel the common factor of $\cos^{2} (θ)$ .

Cancel the common factor.

$\frac{1}{\cos^{2} (θ)} \cdot \cos^{2} (θ)$

Rewrite the expression.

$1$

$1$

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