Precalculus Examples

cos (x) + tan (x) sin (x)

$\cos (x) + \tan (x) \sin (x)$

Step 1

Simplify each term.

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Step 1.1

Rewrite

tan (x)

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

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

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

Step 1.2

Multiply

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

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

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Step 1.2.1

Combine

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

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

sin (x)

$\sin (x)$ .

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

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

Step 1.2.2

Raise

sin (x)

$\sin (x)$ to the power of

1

$1$ .

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

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

Step 1.2.3

Raise

sin (x)

$\sin (x)$ to the power of

1

$1$ .

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

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

Step 1.2.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 1.2.5

Add

1

$1$ and

1

$1$ .

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

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

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

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

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

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

Step 2

Simplify each term.

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Step 2.1

Factor

sin (x)

$\sin (x)$ out of

{sin}^{2} (x)

$\sin^{2} (x)$ .

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

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

Step 2.2

Separate fractions.

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

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

Step 2.3

Convert from

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

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

tan (x)

$\tan (x)$ .

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

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

Step 2.4

Divide

sin (x)

$\sin (x)$ by

1

$1$ .

cos (x) + sin (x) tan (x)

$\cos (x) + \sin (x) \tan (x)$

cos (x) + sin (x) tan (x)

$\cos (x) + \sin (x) \tan (x)$