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

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

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

tan (\frac{π}{4} + \frac{2 π}{3})

- 2 + 3

Solution steps

tan (\frac{π}{4} + \frac{2 π}{3})

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

\frac{1}{4} sin (0)

\frac{2}{tan ( 3 0 ^{\circ} )}

cos (4 5^{\circ}) (sec (4 5^{\circ}) - cos (4 5^{\circ}))

cos (12 0^{\circ}) cos (4 5^{\circ}) - sin (12 0^{\circ}) sin (4 5^{\circ})

4 sin (\frac{π}{4}) cos (\frac{π}{4})

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