What is the value of sin((3pi)/5)cos((3pi)/5) ?

The value of sin((3pi)/5)cos((3pi)/5) is -(sqrt(2)sqrt(5-\sqrt{5)})/8

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sin((3pi)/5)cos((3pi)/5)

sin (\frac{3 π}{5}) cos (\frac{3 π}{5})

- \frac{2 5 - 5}{8}

Solution steps

sin (\frac{3 π}{5}) cos (\frac{3 π}{5})

Rewrite using trig identities:

\frac{sin ( \frac{6 π}{5} )}{2}

= \frac{sin ( \frac{6 π}{5} )}{2}

Rewrite using trig identities:

sin (\frac{6 π}{5}) = - \frac{2 5 - 5}{4}

= \frac{- \frac{2 5 - 5}{4}}{2}

Simplify

\frac{- \frac{2 5 - 5}{4}}{2} : - \frac{2 5 - 5}{8}

= - \frac{2 5 - 5}{8}

sec (10 π)

arccos (cos (\frac{9 π}{5}))

\frac{6}{cos ( 7 2 ^{\circ} )}

400 \cdot sin (3 0^{\circ})

sin^{2} (2 6^{\circ})

What is the value of sin((3pi)/5)cos((3pi)/5) ?
The value of sin((3pi)/5)cos((3pi)/5) is -(sqrt(2)sqrt(5-\sqrt{5)})/8