Algebra Examples

$\cos (θ) \cdot \sec^{2} (θ)$

Step 1

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

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

One to any power is one.

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

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

Step 3

Cancel the common factor of $\cos (θ)$ .

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Step 3.1

Factor $\cos (θ)$ out of $\cos^{2} (θ)$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{1}{\cos (θ)}$

$\frac{1}{\cos (θ)}$

Step 4

Convert from $\frac{1}{\cos (θ)}$ to $\sec (θ)$ .

$\sec (θ)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$