What is the value of sin(120)cos(60)-cos(120)sin(60) ?

The value of sin(120)cos(60)-cos(120)sin(60) is (sqrt(3))/2

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sin(120)cos(60)-cos(120)sin(60)

sin (12 0^{\circ}) cos (6 0^{\circ}) - cos (12 0^{\circ}) sin (6 0^{\circ})

\frac{3}{2}

Solution steps

sin (12 0^{\circ}) cos (6 0^{\circ}) - cos (12 0^{\circ}) sin (6 0^{\circ})

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

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

Simplify

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

= \frac{3}{2}

2 arctan (0)

sin (2 \cdot 30)

arctan (\frac{- 1}{- 1})

- sin (3)

- 4 cos (\frac{π}{3})

What is the value of sin(120)cos(60)-cos(120)sin(60) ?
The value of sin(120)cos(60)-cos(120)sin(60) is (sqrt(3))/2