Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

$\frac{1 - \tan (0)}{1 - \tan (\frac{π}{4}) \tan (π)}$

Step 1.3

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

$\frac{1 - 0}{1 - \tan (\frac{π}{4}) \tan (π)}$

Step 1.4

Multiply $- 1$ by $0$ .

$\frac{1 + 0}{1 - \tan (\frac{π}{4}) \tan (π)}$

Step 1.5

Add $1$ and $0$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{1}{1 - 1 \cdot 1 \tan (π)}$

Step 2.2

Multiply $- 1$ by $1$ .

$\frac{1}{1 - 1 \tan (π)}$

Step 2.3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

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

Step 2.4

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

$\frac{1}{1 - 1 (- 0)}$

Step 2.5

Multiply $- 1 (- 0)$ .

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Step 2.5.1

Multiply $- 1$ by $0$ .

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

Step 2.5.2

Multiply $- 1$ by $0$ .

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

Step 2.6

Add $1$ and $0$ .

$\frac{1}{1}$

Step 3

Cancel the common factor of $1$ .

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Step 3.1

Cancel the common factor.

$\frac{1}{1}$

Step 3.2

Rewrite the expression.

$1$