What is the value of tan((2pi)/3+pi/4) ?

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

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tan((2pi)/3+pi/4)

tan (\frac{2 π}{3} + \frac{π}{4})

- 2 + 3

Solution steps

tan (\frac{2 π}{3} + \frac{π}{4})

Rewrite using trig identities:

\frac{tan ( \frac{2 π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{2 π}{3} ) tan ( \frac{π}{4} )}

= \frac{tan ( \frac{2 π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{2 π}{3} ) tan ( \frac{π}{4} )}

Rewrite using trig identities:

tan (\frac{2 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

tan (0.24 π)

\frac{50}{tan ( 2 0 ^{\circ} )}

4 sec (4) (e^{4} + e^{4} tan (4))

cos (\frac{7 π}{6}) + i sin (\frac{7 π}{6})

\frac{1 - cos ( 0.01 )}{0.01}

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