What is the value of cos((19pi)/(30))cos(pi/5)-sin((19pi)/(30))sin(pi/5) ?

The value of cos((19pi)/(30))cos(pi/5)-sin((19pi)/(30))sin(pi/5) is -(sqrt(3))/2

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cos((19pi)/(30))cos(pi/5)-sin((19pi)/(30))sin(pi/5)

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

- \frac{3}{2}

Solution steps

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

Rewrite using trig identities:

cos (\frac{5 π}{6})

= cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

= - \frac{3}{2}

sec (85 5^{\circ})

sin (9 3^{\circ})

3 cos (\frac{4 π}{3})

tan (0.5 π)

tan (58.8 3^{\circ})

What is the value of cos((19pi)/(30))cos(pi/5)-sin((19pi)/(30))sin(pi/5) ?
The value of cos((19pi)/(30))cos(pi/5)-sin((19pi)/(30))sin(pi/5) is -(sqrt(3))/2