Trigonometry Examples

$\frac{\cot^{2} (x)}{\csc (x)} - \csc (x)$

Step 1

Separate fractions.

$\frac{\cot^{2} (x)}{1} \cdot \frac{1}{\csc (x)} - \csc (x)$

Step 2

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

$\frac{\cot^{2} (x)}{1} \cdot \frac{1}{\frac{1}{\sin (x)}} - \csc (x)$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

$\frac{\cot^{2} (x)}{1} (1 \sin (x)) - \csc (x)$

Step 4

Multiply $\sin (x)$ by $1$ .

$\frac{\cot^{2} (x)}{1} \sin (x) - \csc (x)$

Step 5

Divide $\cot^{2} (x)$ by $1$ .

$\cot^{2} (x) \sin (x) - \csc (x)$

Step 6

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

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

Step 7

Apply the product rule to $\frac{\cos (x)}{\sin (x)}$ .

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Cancel the common factor.

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

Step 8.3

Rewrite the expression.

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

Step 9

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

$\frac{\cos (x) \cos (x)}{\sin (x)} - \csc (x)$

Step 10

Separate fractions.

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

Step 11

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

$\frac{\cos (x)}{1} \cot (x) - \csc (x)$

Step 12

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

$\cos (x) \cot (x) - \csc (x)$