What is the value of tan(pi/4+pi/3) ?

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

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tan(pi/4+pi/3)

tan (\frac{π}{4} + \frac{π}{3})

- 2 - 3

Solution steps

tan (\frac{π}{4} + \frac{π}{3})

Rewrite using trig identities:

\frac{tan ( \frac{π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{π}{3} ) tan ( \frac{π}{4} )}

= \frac{tan ( \frac{π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{π}{3} ) tan ( \frac{π}{4} )}

Use the following trivial identity:

tan (\frac{π}{3}) = 3

Use the following trivial identity:

tan (\frac{π}{4}) = 1

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

Simplify

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

= - 2 - 3

\frac{10}{sin ( 6 0 ^{\circ} )}

sin^{2} (13 5^{\circ})

\frac{- sec ^{2} ( \frac{π}{4} )}{4 cos ( \frac{π}{4} )}

7 cos (6 0^{\circ})

sin (arccos (- \frac{1}{3}))