Trigonometry Examples

$\tan (2 π - 0)$

Step 1

Use the difference formula for tangent to simplify the expression. The formula states that $\tan (A - B) = \frac{\tan (A) - \tan (B)}{1 + \tan (A) \tan (B)}$ .

$\frac{\tan (2 π) - \tan (0)}{1 + \tan (2 π) \tan (0)}$

Step 2

Remove parentheses.

$\frac{\tan (2 π) - \tan (0)}{1 + \tan (2 π) \tan (0)}$

Step 3

Simplify the numerator.

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Step 3.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{\tan (0) - \tan (0)}{1 + \tan (2 π) \tan (0)}$

Step 3.2

The exact value of $\tan (0)$ is $0$ .

$\frac{0 - \tan (0)}{1 + \tan (2 π) \tan (0)}$

Step 3.3

The exact value of $\tan (0)$ is $0$ .

$\frac{0 - 0}{1 + \tan (2 π) \tan (0)}$

Step 3.4

Multiply $- 1$ by $0$ .

$\frac{0 + 0}{1 + \tan (2 π) \tan (0)}$

Step 3.5

Add $0$ and $0$ .

$\frac{0}{1 + \tan (2 π) \tan (0)}$

Step 4

Simplify the denominator.

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Step 4.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{0}{1 + \tan (0) \tan (0)}$

Step 4.2

The exact value of $\tan (0)$ is $0$ .

$\frac{0}{1 + 0 \tan (0)}$

Step 4.3

The exact value of $\tan (0)$ is $0$ .

$\frac{0}{1 + 0 \cdot 0}$

Step 4.4

Multiply $0$ by $0$ .

$\frac{0}{1 + 0}$

Step 4.5

Add $1$ and $0$ .

$\frac{0}{1}$

Step 5

Divide $0$ by $1$ .

$0$