Evaluate tan(x)-(sec(x)^2)/(tan(x))

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

Separate fractions.

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

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

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

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

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

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

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

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

$\tan (x) - (\sec^{2} (x) \cot (x))$

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

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

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

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

Apply the product rule to $\frac{1}{\cos (x)}$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Separate fractions.

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

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

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

Separate fractions.

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

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

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

Divide $1^{2}$ by $1$ .

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

One to any power is one.

$\tan (x) - (1 \csc (x) \sec (x))$

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

$\tan (x) - \csc (x) \sec (x)$