Trigonometry Examples

$2 \cos (x) (3 - 7 \tan (x))$

Step 1

Simplify each term.

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Step 1.1

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

$2 \cos (x) (3 - 7 \frac{\sin (x)}{\cos (x)})$

Step 1.2

Combine $- 7$ and $\frac{\sin (x)}{\cos (x)}$ .

$2 \cos (x) (3 + \frac{- 7 \sin (x)}{\cos (x)})$

Step 1.3

Move the negative in front of the fraction.

$2 \cos (x) (3 - \frac{7 \sin (x)}{\cos (x)})$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$2 \cos (x) \cdot 3 + 2 \cos (x) (- \frac{7 \sin (x)}{\cos (x)})$

Step 2.2

Multiply $3$ by $2$ .

$6 \cos (x) + 2 \cos (x) (- \frac{7 \sin (x)}{\cos (x)})$

Step 2.3

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

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Step 2.3.1

Move the leading negative in $- \frac{7 \sin (x)}{\cos (x)}$ into the numerator.

$6 \cos (x) + 2 \cos (x) \frac{- 7 \sin (x)}{\cos (x)}$

Step 2.3.2

Factor $\cos (x)$ out of $2 \cos (x)$ .

$6 \cos (x) + \cos (x) \cdot 2 \frac{- 7 \sin (x)}{\cos (x)}$

Step 2.3.3

Cancel the common factor.

$6 \cos (x) + \cos (x) \cdot 2 \frac{- 7 \sin (x)}{\cos (x)}$

Step 2.3.4

Rewrite the expression.

$6 \cos (x) + 2 (- 7 \sin (x))$

Step 2.4

Multiply $- 7$ by $2$ .

$6 \cos (x) - 14 \sin (x)$