Trigonometry Examples

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

Step 1

Start on the left side.

$\tan (\frac{π}{4} - x)$

Step 2

Apply the difference of angles identity.

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

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

Simplify the denominator.

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$\tan (\frac{π}{4} - x) = \frac{1 - \tan (x)}{1 + \tan (x)}$ is an identity