Trigonometry Examples

$\tan (x + \frac{π}{4})$

Step 1

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

$\frac{\tan (x) + \tan (\frac{π}{4})}{1 - \tan (x) \tan (\frac{π}{4})}$

Step 2

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\frac{\tan (x) + 1}{1 - \tan (x) \tan (\frac{π}{4})}$

Step 3

Simplify the denominator.

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Step 3.1

The exact value of $\tan (\frac{π}{4})$ is $1$ .

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

Step 3.2

Multiply $- 1$ by $1$ .

$\frac{\tan (x) + 1}{1 - \tan (x)}$