Algebra Examples

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

Step 1

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

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Multiply $\frac{1}{\cos (θ)}$ by $\frac{1}{\sin (θ)}$ .

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

Step 4

Apply pythagorean identity.

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

Step 5

Simplify terms.

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Step 5.1

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

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Step 5.1.1

Factor $\sin (θ)$ out of $\cos (θ) \sin (θ)$ .

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

Step 5.1.2

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

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

Step 5.1.3

Cancel the common factor.

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

Step 5.1.4

Rewrite the expression.

$\frac{1}{\cos (θ)} \cdot \sin (θ)$

Step 5.2

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

$\frac{\sin (θ)}{\cos (θ)}$

Step 6

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

$\tan (θ)$