Finite Math Examples

$\tan (80) \cdot \sec (10) \cdot \cos (80)$

Step 1

Rewrite $\tan (80)$ in terms of sines and cosines.

$\frac{\sin (80)}{\cos (80)} \cdot \sec (10) \cdot \cos (80)$

Step 2

Rewrite $\sec (10)$ in terms of sines and cosines.

$\frac{\sin (80)}{\cos (80)} \cdot \frac{1}{\cos (10)} \cdot \cos (80)$

Step 3

Multiply $\frac{\sin (80)}{\cos (80)}$ by $\frac{1}{\cos (10)}$ .

$\frac{\sin (80)}{\cos (80) \cos (10)} \cdot \cos (80)$

Step 4

Cancel the common factor of $\cos (80)$ .

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Step 4.1

Factor $\cos (80)$ out of $\cos (80) \cos (10)$ .

$\frac{\sin (80)}{\cos (80) (\cos (10))} \cdot \cos (80)$

Step 4.2

Cancel the common factor.

$\frac{\sin (80)}{\cos (80) \cos (10)} \cdot \cos (80)$

Step 4.3

Rewrite the expression.

$\frac{\sin (80)}{\cos (10)}$

Step 5

Rewrite $\frac{\sin (80)}{\cos (10)}$ as a product.

$\sin (80) \frac{1}{\cos (10)}$

Step 6

Write $\sin (80)$ as a fraction with denominator $1$ .

$\frac{\sin (80)}{1} \cdot \frac{1}{\cos (10)}$

Step 7

Simplify.

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Step 7.1

Divide $\sin (80)$ by $1$ .

$\sin (80) \frac{1}{\cos (10)}$

Step 7.2

Convert from $\frac{1}{\cos (10)}$ to $\sec (10)$ .

$\sin (80) \sec (10)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\sin (80) \sec (10)$

Decimal Form:

$1$