Trigonometry Examples

$\frac{4 \cos (1)}{\cos^{2} (1) - 1}$

Step 1

Simplify with factoring out.

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Step 1.1

Reorder $\cos^{2} (1)$ and $- 1$ .

$\frac{4 \cos (1)}{- 1 + \cos^{2} (1)}$

Step 1.2

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{4 \cos (1)}{- 1 (1) + \cos^{2} (1)}$

Step 1.3

Factor $- 1$ out of $\cos^{2} (1)$ .

$\frac{4 \cos (1)}{- 1 (1) - 1 (- \cos^{2} (1))}$

Step 1.4

Factor $- 1$ out of $- 1 (1) - 1 (- \cos^{2} (1))$ .

$\frac{4 \cos (1)}{- 1 (1 - \cos^{2} (1))}$

Step 1.5

Rewrite $- 1 (1 - \cos^{2} (1))$ as $- (1 - \cos^{2} (1))$ .

$\frac{4 \cos (1)}{- (1 - \cos^{2} (1))}$

Step 2

Apply pythagorean identity.

$\frac{4 \cos (1)}{- \sin^{2} (1)}$

Step 3

Factor $\sin (1)$ out of $\sin^{2} (1)$ .

$\frac{4 \cos (1)}{- (\sin (1) \sin (1))}$

Step 4

Separate fractions.

$\frac{4}{- (\sin (1))} \cdot \frac{\cos (1)}{\sin (1)}$

Step 5

Convert from $\frac{\cos (1)}{\sin (1)}$ to $\cot (1)$ .

$\frac{4}{- (\sin (1))} \cot (1)$

Step 6

Separate fractions.

$\frac{4}{- 1} \cdot \frac{1}{\sin (1)} \cot (1)$

Step 7

Convert from $\frac{1}{\sin (1)}$ to $\csc (1)$ .

$\frac{4}{- 1} \csc (1) \cot (1)$

Step 8

Divide $4$ by $- 1$ .

$- 4 \csc (1) \cot (1)$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- 4 \csc (1) \cot (1)$

Decimal Form:

$- 13130.55866229 \dots$