Trigonometry Examples

$\frac{1}{\tan^{2} (x)}$

Step 1

Rewrite $1$ as $1^{2}$ .

$\frac{1^{2}}{\tan^{2} (x)}$

Step 2

Rewrite $\frac{1^{2}}{\tan^{2} (x)}$ as ${(\frac{1}{\tan (x)})}^{2}$ .

${(\frac{1}{\tan (x)})}^{2}$

Step 3

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

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

Step 4

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

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

Step 5

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

$\cot^{2} (x)$