What is the value of 2sin((2pi)/5)cos((2pi)/5) ?

The value of 2sin((2pi)/5)cos((2pi)/5) is (sqrt(2)sqrt(5-\sqrt{5)})/4

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2sin((2pi)/5)cos((2pi)/5)

2 sin (\frac{2 π}{5}) cos (\frac{2 π}{5})

\frac{2 5 - 5}{4}

Solution steps

2 sin (\frac{2 π}{5}) cos (\frac{2 π}{5})

Rewrite using trig identities:

sin (\frac{4 π}{5})

= sin (\frac{4 π}{5})

Rewrite using trig identities:

sin (\frac{π}{5})

= sin (\frac{π}{5})

Rewrite using trig identities:

\frac{2 5 - 5}{4}

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

\frac{sin ( 84 0 ^{\circ} )}{cos ( 33 0 ^{\circ} ) + sin ( 31 5 ^{\circ} )}

cos (arctan (3) + arcsin (\frac{1}{3}))

tan (\frac{5 π}{6} - \frac{5 π}{4})

sin (arcsec (8))

- arctan (3)

What is the value of 2sin((2pi)/5)cos((2pi)/5) ?
The value of 2sin((2pi)/5)cos((2pi)/5) is (sqrt(2)sqrt(5-\sqrt{5)})/4