Precalculus Examples

$\cos (x) \sin (x) (\cot (x) + \sec (x))$

Simplify each term.

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

$\cos (x) \sin (x) (\frac{\cos (x)}{\sin (x)} + \sec (x))$

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

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

Simplify terms.

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Apply the distributive property.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Cancel the common factor of $\cos (x)$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$\cos^{2} (x) + \sin (x)$