Algebra Examples

$\frac{\sin (θ) \sec (θ)}{\cos^{2} (θ)}$

Step 1

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

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

Step 2

Combine $\sin (θ)$ and $\frac{1}{\cos (θ)}$ .

$\frac{\frac{\sin (θ)}{\cos (θ)}}{\cos^{2} (θ)}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Combine.

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

Step 5

Multiply $\cos (θ)$ by $\cos^{2} (θ)$ by adding the exponents.

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Step 5.1

Multiply $\cos (θ)$ by $\cos^{2} (θ)$ .

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Step 5.1.1

Raise $\cos (θ)$ to the power of $1$ .

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

Step 5.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 5.2

Add $1$ and $2$ .

$\frac{\sin (θ) \cdot 1}{\cos^{3} (θ)}$

Step 6

Multiply $\sin (θ)$ by $1$ .

$\frac{\sin (θ)}{\cos^{3} (θ)}$

Step 7

Factor $\cos (θ)$ out of $\cos^{3} (θ)$ .

$\frac{\sin (θ)}{\cos (θ) \cos^{2} (θ)}$

Step 8

Separate fractions.

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

Step 9

Convert from $\frac{\sin (θ)}{\cos (θ)}$ to $\tan (θ)$ .

$\frac{1}{\cos^{2} (θ)} \tan (θ)$

Step 10

Rewrite $1$ as $1^{2}$ .

$\frac{1^{2}}{\cos^{2} (θ)} \tan (θ)$

Step 11

Rewrite $\frac{1^{2}}{\cos^{2} (θ)}$ as ${(\frac{1}{\cos (θ)})}^{2}$ .

${(\frac{1}{\cos (θ)})}^{2} \tan (θ)$

Step 12

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

$\sec^{2} (θ) \tan (θ)$