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

The value of cos(pi/4+(2pi)/3) is (sqrt(2)(-1-sqrt(3)))/4

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

cos (\frac{π}{4} + \frac{2 π}{3})

\frac{2 ( - 1 - 3 )}{4}

Solution steps

cos (\frac{π}{4} + \frac{2 π}{3})

Rewrite using trig identities:

cos (\frac{2 π}{3}) cos (\frac{π}{4}) - sin (\frac{2 π}{3}) sin (\frac{π}{4})

= cos (\frac{2 π}{3}) cos (\frac{π}{4}) - sin (\frac{2 π}{3}) sin (\frac{π}{4})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

= (- \frac{1}{2}) \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2}

Simplify

(- \frac{1}{2}) \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2} : \frac{2 ( - 1 - 3 )}{4}

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

sin (8 5^{\circ}) cos (2 5^{\circ}) - sin (2 5^{\circ}) cos (8 5^{\circ})

1 + 2 cos (π)

cos (2 \cdot \frac{3 π}{2})

9 sin (3 0^{\circ})

cos (- \frac{2}{5})

What is the value of cos(pi/4+(2pi)/3) ?
The value of cos(pi/4+(2pi)/3) is (sqrt(2)(-1-sqrt(3)))/4