What is the value of tan(pi/4+pi/6) ?

The value of tan(pi/4+pi/6) is 2+sqrt(3)

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tan(pi/4+pi/6)

tan (\frac{π}{4} + \frac{π}{6})

2 + 3

Solution steps

tan (\frac{π}{4} + \frac{π}{6})

Rewrite using trig identities:

\frac{tan ( \frac{π}{4} ) + tan ( \frac{π}{6} )}{1 - tan ( \frac{π}{4} ) tan ( \frac{π}{6} )}

= \frac{tan ( \frac{π}{4} ) + tan ( \frac{π}{6} )}{1 - tan ( \frac{π}{4} ) tan ( \frac{π}{6} )}

Use the following trivial identity:

tan (\frac{π}{4}) = 1

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

= \frac{1 + \frac{3}{3}}{1 - 1 \cdot \frac{3}{3}}

Simplify

\frac{1 + \frac{3}{3}}{1 - 1 \cdot \frac{3}{3}} : 2 + 3

= 2 + 3

arccos (\frac{2}{20})

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