Trigonometry Examples

\frac{cos (x) tan (x) - sin (x)}{cot (x)} = 0

$\frac{\cos (x) \tan (x) - \sin (x)}{\cot (x)} = 0$

Step 1

Set the numerator equal to zero.

cos (x) tan (x) - sin (x) = 0

$\cos (x) \tan (x) - \sin (x) = 0$

Step 2

Solve the equation for

x

$x$ .

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Step 2.1

Divide each term in the equation by

cos (x)

$\cos (x)$ .

\frac{cos (x) tan (x)}{cos (x)} + \frac{- sin (x)}{cos (x)} = \frac{0}{cos (x)}

$\frac{\cos (x) \tan (x)}{\cos (x)} + \frac{- \sin (x)}{\cos (x)} = \frac{0}{\cos (x)}$

Step 2.2

Cancel the common factor of

cos (x)

$\cos (x)$ .

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Step 2.2.1

Cancel the common factor.

$\frac{\cos (x) \tan (x)}{\cos (x)} + \frac{- \sin (x)}{\cos (x)} = \frac{0}{\cos (x)}$

Step 2.2.2

Divide

$\tan (x)$ by

$1$ .

$\tan (x) + \frac{- \sin (x)}{\cos (x)} = \frac{0}{\cos (x)}$

Step 2.3

Rewrite

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

$\frac{\sin (x)}{\cos (x)} + \frac{- \sin (x)}{\cos (x)} = \frac{0}{\cos (x)}$

Step 2.4

Convert from

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

$\tan (x)$ .

$\tan (x) + \frac{- \sin (x)}{\cos (x)} = \frac{0}{\cos (x)}$

Step 2.5

Separate fractions.

$\tan (x) + \frac{- 1}{1} \cdot \frac{\sin (x)}{\cos (x)} = \frac{0}{\cos (x)}$

Step 2.6

Convert from

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

$\tan (x)$ .

$\tan (x) + \frac{- 1}{1} \cdot \tan (x) = \frac{0}{\cos (x)}$

Step 2.7

Divide

$- 1$ by

$1$ .

$\tan (x) - \tan (x) = \frac{0}{\cos (x)}$

Step 2.8

Separate fractions.

$\tan (x) - \tan (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

Step 2.9

Convert from

$\frac{1}{\cos (x)}$ to

$\sec (x)$ .

$\tan (x) - \tan (x) = \frac{0}{1} \cdot \sec (x)$

Step 2.10

Divide

$0$ by

$1$ .

$\tan (x) - \tan (x) = 0 \sec (x)$

Step 2.11

Multiply

$0$ by

$\sec (x)$ .

$\tan (x) - \tan (x) = 0$

Step 2.12

Subtract

$\tan (x)$ from

$\tan (x)$ .

$0 = 0$

Step 2.13

Since

$0 = 0$ , the equation will always be true for any value of

$x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$