Precalculus Examples

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

Step 1

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

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

Step 2

Rewrite $\csc (x - 1)$ in terms of sines and cosines.

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

Step 3

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

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

Step 4

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

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

Step 5

Convert from $\frac{\sin (x) \sin (x - 1)}{\cos (x)}$ to $\sin (x) \tan (x)$ .

${(\sin (x) \tan (x))}^{2}$

Step 6

Apply the product rule to $\sin (x) \tan (x)$ .

$\sin^{2} (x) \tan^{2} (x)$