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

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

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

2 sin (\frac{π}{5}) cos (\frac{π}{5})

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

Solution steps

2 sin (\frac{π}{5}) cos (\frac{π}{5})

Rewrite using trig identities:

sin (\frac{π}{5}) = \frac{2 5 - 5}{4}

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

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

Simplify

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

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

cos (12 0^{\circ}) + sin (15 0^{\circ})

tan (\frac{1}{6})

arcsin (cos (30 0^{\circ}))

arcsin (\frac{2}{2.5})

cos (3 0^{\circ}) tan (3 0^{\circ})

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