Trigonometry Examples

$\sec (x) - \sin (x) \cdot \tan (x)$

Simplify terms.

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Simplify each term.

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

$\frac{1}{\cos (x)} - \sin (x) \cdot \tan (x)$

Rewrite $\tan (x)$ in terms of sines and cosines.

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

Multiply $- \sin (x) \frac{\sin (x)}{\cos (x)}$ .

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Raise $\sin (x)$ to the power of $1$ .

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

Raise $\sin (x)$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Combine fractions with similar denominators.

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

Apply pythagorean identity.

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

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

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

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

Cancel the common factors.

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Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$\cos (x)$

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