What is the value of 2cos(pi/6)-4sin(pi/6) ?

The value of 2cos(pi/6)-4sin(pi/6) is sqrt(3)-2

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2cos(pi/6)-4sin(pi/6)

2 cos (\frac{π}{6}) - 4 sin (\frac{π}{6})

3 - 2

Solution steps

2 cos (\frac{π}{6}) - 4 sin (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= 2 \cdot \frac{3}{2} - 4 \cdot \frac{1}{2}

Simplify

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

= 3 - 2

cos^{2} (3 π)

sin^{2} (\frac{1}{4} π)

cot (6 2^{\circ})

cos (\frac{13}{12})

cos (\frac{19 π}{30}) cos (\frac{π}{5}) - sin (\frac{19 π}{30}) sin (\frac{π}{5})

What is the value of 2cos(pi/6)-4sin(pi/6) ?
The value of 2cos(pi/6)-4sin(pi/6) is sqrt(3)-2