What is the value of sin((5pi)/(12))cos(pi/(12)) ?

The value of sin((5pi)/(12))cos(pi/(12)) is (2+sqrt(3))/4

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sin((5pi)/(12))cos(pi/(12))

sin (\frac{5 π}{12}) cos (\frac{π}{12})

\frac{2 + 3}{4}

Solution steps

sin (\frac{5 π}{12}) cos (\frac{π}{12})

Rewrite using trig identities:

\frac{sin ( \frac{π}{2} ) + sin ( \frac{π}{3} )}{2}

= \frac{sin ( \frac{π}{2} ) + sin ( \frac{π}{3} )}{2}

Use the following trivial identity:

sin (\frac{π}{2}) = 1

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= \frac{1 + \frac{3}{2}}{2}

Simplify

\frac{1 + \frac{3}{2}}{2} : \frac{2 + 3}{4}

= \frac{2 + 3}{4}

45 sin (6 0^{\circ})

40 sin (2 0^{\circ})

8 sin (0.3) e^{- 0.3} - 1

2 tan (\frac{π}{4}) sec^{2} (\frac{π}{4})

2 sin (3)

What is the value of sin((5pi)/(12))cos(pi/(12)) ?
The value of sin((5pi)/(12))cos(pi/(12)) is (2+sqrt(3))/4