What is the value of 6cos(pi/5)sin(pi/5) ?

The value of 6cos(pi/5)sin(pi/5) is (3sqrt(2)(1+sqrt(5))sqrt(5-\sqrt{5)})/8

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6cos(pi/5)sin(pi/5)

6 cos (\frac{π}{5}) sin (\frac{π}{5})

\frac{3 2 ( 1 + 5 ) 5 - 5}{8}

Solution steps

6 cos (\frac{π}{5}) sin (\frac{π}{5})

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

Rewrite using trig identities:

sin (\frac{π}{5}) = \frac{2 5 - 5}{4}

= 6 \cdot \frac{5 + 1}{4} \cdot \frac{2 5 - 5}{4}

Simplify

6 \cdot \frac{5 + 1}{4} \cdot \frac{2 5 - 5}{4} : \frac{3 2 ( 1 + 5 ) 5 - 5}{8}

= \frac{3 2 ( 1 + 5 ) 5 - 5}{8}

tan (- \frac{5}{4})

\frac{20.2 sin ( 29. 3 ^{\circ} )}{5 cos ( 3 0 ^{\circ} )}

arctan (16666666)

200 cos (3 0^{\circ}) + 500 cos (7 0^{\circ})

16 sin (\frac{2 π}{4})

What is the value of 6cos(pi/5)sin(pi/5) ?
The value of 6cos(pi/5)sin(pi/5) is (3sqrt(2)(1+sqrt(5))sqrt(5-\sqrt{5)})/8