Trigonometry Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $\cos (x)$ by $1$ .

$\cos (x)$