Trigonometry Examples

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

Step 1

Apply pythagorean identity.

$\frac{\cos (x)}{\cos^{2} (x)}$

Step 2

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

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Step 2.1

Multiply by $1$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\frac{1}{\cos (x)}$

Step 3

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

$\sec (x)$

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