Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Apply the distributive property.

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

Step 4

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

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

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

Tap for more steps...

Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

Rewrite using the commutative property of multiplication.

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

Step 7

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

Tap for more steps...

Step 7.1

Move the leading negative in $- \frac{\sin (x)}{\cos (x)}$ into the numerator.

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

$1 - \sin (x)$