Trigonometry Examples

$\frac{\tan (73) - \tan (13)}{1 + \tan (73) \tan (13)} = \sqrt{B}$

Step 1

Subtract $\sqrt{B}$ from both sides of the equation.

$\frac{\tan (73) - \tan (13)}{1 + \tan (73) \tan (13)} - \sqrt{B} = 0$

Step 2

Simplify each term.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Evaluate $\tan (73)$ .

$\frac{3.27085261 - \tan (13)}{1 + \tan (73) \tan (13)} - \sqrt{B} = 0$

Step 2.1.2

Evaluate $\tan (13)$ .

$\frac{3.27085261 - 1 \cdot 0.23086819}{1 + \tan (73) \tan (13)} - \sqrt{B} = 0$

Step 2.1.3

Multiply $- 1$ by $0.23086819$ .

$\frac{3.27085261 - 0.23086819}{1 + \tan (73) \tan (13)} - \sqrt{B} = 0$

Step 2.1.4

Subtract $0.23086819$ from $3.27085261$ .

$\frac{3.03998442}{1 + \tan (73) \tan (13)} - \sqrt{B} = 0$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Evaluate $\tan (73)$ .

$\frac{3.03998442}{1 + 3.27085261 \tan (13)} - \sqrt{B} = 0$

Step 2.2.2

Evaluate $\tan (13)$ .

$\frac{3.03998442}{1 + 3.27085261 \cdot 0.23086819} - \sqrt{B} = 0$

Step 2.2.3

Multiply $3.27085261$ by $0.23086819$ .

$\frac{3.03998442}{1 + 0.75513582} - \sqrt{B} = 0$

Step 2.2.4

Add $1$ and $0.75513582$ .

$\frac{3.03998442}{1.75513582} - \sqrt{B} = 0$

Step 2.3

Divide $3.03998442$ by $1.75513582$ .

$1.7320508 - \sqrt{B} = 0$

Step 3

Set the radicand in $\sqrt{B}$ less than $0$ to find where the expression is undefined.

$B < 0$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$B < 0$

$(- \infty, 0)$

Step 5