Trigonometry Examples

$\tan (u - \frac{π}{4})$

Step 1

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

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

Step 2

Remove parentheses.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

Multiply $- 1$ by $1$ .

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

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

Multiply $\tan (u)$ by $1$ .

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