What is the value of cos(60)cos(30)-sin(60)sin(30) ?

The value of cos(60)cos(30)-sin(60)sin(30) is 0

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cos(60)cos(30)-sin(60)sin(30)

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

0

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

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

Simplify

= 0

cos^{2} (157. 5^{\circ}) - sin^{2} (157. 5^{\circ})

arccos (sin (- \frac{5 π}{6}))

arcsin (sin (- \frac{3 π}{4}))

30 \cdot cos (4 5^{\circ})

sin (\frac{9}{4} π)

What is the value of cos(60)cos(30)-sin(60)sin(30) ?
The value of cos(60)cos(30)-sin(60)sin(30) is 0