What is the value of cos((23pi)/(24))sin((17pi)/(24)) ?

The value of cos((23pi)/(24))sin((17pi)/(24)) is (-sqrt(3)-sqrt(2))/4

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cos((23pi)/(24))sin((17pi)/(24))

cos (\frac{23 π}{24}) sin (\frac{17 π}{24})

\frac{- 3 - 2}{4}

Solution steps

cos (\frac{23 π}{24}) sin (\frac{17 π}{24})

Rewrite using trig identities:

\frac{sin ( \frac{5 π}{3} ) - sin ( \frac{π}{4} )}{2}

= \frac{sin ( \frac{5 π}{3} ) - sin ( \frac{π}{4} )}{2}

Rewrite using trig identities:

sin (\frac{5 π}{3}) = - \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

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

sin (2 arccos (\frac{1}{5}))

800 sin (4 5^{\circ})

cos (\frac{π}{4} - 2 π)

cos^{2} (3 6^{\circ}) - sin^{2} (3 6^{\circ})

csc (\frac{11 π}{12})

What is the value of cos((23pi)/(24))sin((17pi)/(24)) ?
The value of cos((23pi)/(24))sin((17pi)/(24)) is (-sqrt(3)-sqrt(2))/4