What is the value of sin((5pi)/(24))cos(pi/(24)) ?

The value of sin((5pi)/(24))cos(pi/(24)) is (sqrt(2)+1)/4

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sin((5pi)/(24))cos(pi/(24))

sin (\frac{5 π}{24}) cos (\frac{π}{24})

\frac{2 + 1}{4}

Solution steps

sin (\frac{5 π}{24}) cos (\frac{π}{24})

Rewrite using trig identities:

\frac{sin ( \frac{π}{4} ) + sin ( \frac{π}{6} )}{2}

= \frac{sin ( \frac{π}{4} ) + sin ( \frac{π}{6} )}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= \frac{\frac{2}{2} + \frac{1}{2}}{2}

Simplify

\frac{\frac{2}{2} + \frac{1}{2}}{2} : \frac{2 + 1}{4}

= \frac{2 + 1}{4}

2 cos (\frac{5 π}{3}) + cos^{2} (\frac{5 π}{3})

sin (0.1 π)

sin (13. 5^{\circ})

- 2 sin (\frac{7 π}{4})

arcsin (\frac{10}{16})

What is the value of sin((5pi)/(24))cos(pi/(24)) ?
The value of sin((5pi)/(24))cos(pi/(24)) is (sqrt(2)+1)/4