Trigonometry Examples

$\tan (\frac{π}{4} + x)$

Step 1

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

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

Multiply $- 1$ by $1$ .

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

Step 3.3

Rewrite $- 1 \tan (x)$ as $- \tan (x)$ .

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