What is the value of 2cos((5pi)/6)+sin(2((5pi)/6)) ?

The value of 2cos((5pi)/6)+sin(2((5pi)/6)) is -sqrt(3)-(sqrt(3))/2

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2cos((5pi)/6)+sin(2((5pi)/6))

2 cos (\frac{5 π}{6}) + sin (2 (\frac{5 π}{6}))

- 3 - \frac{3}{2}

Solution steps

2 cos (\frac{5 π}{6}) + sin (2 (\frac{5 π}{6}))

= 2 cos (\frac{5 π}{6}) + sin (2 \cdot \frac{5 π}{6})

Rewrite using trig identities:

sin (2 \cdot \frac{5 π}{6}) = 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

= 2 cos (\frac{5 π}{6}) + 2 sin (\frac{5 π}{6}) cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

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

Simplify

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

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

\frac{1 - cos ( 3 ( 0.999 ) - 3 )}{5 ( ( 0.999 ) - 1 ) ^{2}}

sin (6 0^{\circ}) - sin (3 0^{\circ})

- \frac{1}{4} sin (2 π)

14 sin (3 5^{\circ})

8 cos (\frac{7 π}{6})

What is the value of 2cos((5pi)/6)+sin(2((5pi)/6)) ?
The value of 2cos((5pi)/6)+sin(2((5pi)/6)) is -sqrt(3)-(sqrt(3))/2