Trigonometry Examples

$(\tan (\frac{5 π}{18} - x) + \tan (\frac{2 π}{9} + x)) \div (1 - \tan (\frac{5 π}{18} - x) \tan (\frac{3 π}{9} + x))$

Step 1

Rewrite the division as a fraction.

$\frac{\tan (\frac{5 π}{18} - x) + \tan (\frac{2 π}{9} + x)}{1 - \tan (\frac{5 π}{18} - x) \tan (\frac{3 π}{9} + x)}$

Step 2

Cancel the common factor of $3$ and $9$ .

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Step 2.1

Factor $3$ out of $3 π$ .

$\frac{\tan (\frac{5 π}{18} - x) + \tan (\frac{2 π}{9} + x)}{1 - \tan (\frac{5 π}{18} - x) \tan (\frac{3 (π)}{9} + x)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $9$ .

$\frac{\tan (\frac{5 π}{18} - x) + \tan (\frac{2 π}{9} + x)}{1 - \tan (\frac{5 π}{18} - x) \tan (\frac{3 π}{3 \cdot 3} + x)}$

Step 2.2.2

Cancel the common factor.

$\frac{\tan (\frac{5 π}{18} - x) + \tan (\frac{2 π}{9} + x)}{1 - \tan (\frac{5 π}{18} - x) \tan (\frac{3 π}{3 \cdot 3} + x)}$

Step 2.2.3

Rewrite the expression.

$\frac{\tan (\frac{5 π}{18} - x) + \tan (\frac{2 π}{9} + x)}{1 - \tan (\frac{5 π}{18} - x) \tan (\frac{π}{3} + x)}$