What is the value of cos((2pi)/3)+sin((2pi)/3) ?

The value of cos((2pi)/3)+sin((2pi)/3) is (-1+sqrt(3))/2

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cos((2pi)/3)+sin((2pi)/3)

cos (\frac{2 π}{3}) + sin (\frac{2 π}{3})

\frac{- 1 + 3}{2}

Solution steps

cos (\frac{2 π}{3}) + sin (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

= - \frac{1}{2} + \frac{3}{2}

Simplify

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

= \frac{- 1 + 3}{2}

csc (- \frac{7 π}{3})

csc (6 π)

tan (\frac{25 π}{4})

e^{- 1} sin (1)

cos^{2} (4 5^{\circ}) + sin^{2} (4 5^{\circ})

What is the value of cos((2pi)/3)+sin((2pi)/3) ?
The value of cos((2pi)/3)+sin((2pi)/3) is (-1+sqrt(3))/2