Trigonometry Examples

$\tan (20) - \frac{\cos (70)}{\cos (20)}$

Step 1

Rewrite $\tan (20)$ in terms of sines and cosines.

$\frac{\sin (20)}{\cos (20)} - \frac{\cos (70)}{\cos (20)}$

Step 2

Simplify each term.

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Step 2.1

Convert from $\frac{\sin (20)}{\cos (20)}$ to $\tan (20)$ .

$\tan (20) - \frac{\cos (70)}{\cos (20)}$

Step 2.2

Rewrite $\frac{\cos (70)}{\cos (20)}$ as a product.

$\tan (20) - (\cos (70) \frac{1}{\cos (20)})$

Step 2.3

Write $\cos (70)$ as a fraction with denominator $1$ .

$\tan (20) - (\frac{\cos (70)}{1} \cdot \frac{1}{\cos (20)})$

Step 2.4

Simplify.

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Step 2.4.1

Divide $\cos (70)$ by $1$ .

$\tan (20) - (\cos (70) \frac{1}{\cos (20)})$

Step 2.4.2

Convert from $\frac{1}{\cos (20)}$ to $\sec (20)$ .

$\tan (20) - (\cos (70) \sec (20))$

$\tan (20) - \cos (70) \sec (20)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\tan (20) - \cos (70) \sec (20)$

Decimal Form:

$1.11022302 \cdot 10^{- 16}$