What is the value of sin((3pi)/(10))-sin(pi/(10)) ?

The value of sin((3pi)/(10))-sin(pi/(10)) is (sqrt(2)(1+sqrt(5))sqrt(3-\sqrt{5)})/8

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sin((3pi)/(10))-sin(pi/(10))

sin (\frac{3 π}{10}) - sin (\frac{π}{10})

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

Solution steps

sin (\frac{3 π}{10}) - sin (\frac{π}{10})

Rewrite using trig identities:

2 sin (\frac{π}{10}) cos (\frac{π}{5})

= 2 sin (\frac{π}{10}) cos (\frac{π}{5})

Rewrite using trig identities:

sin (\frac{π}{10}) = \frac{2 3 - 5}{4}

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

= 2 \cdot \frac{2 3 - 5}{4} \cdot \frac{5 + 1}{4}

Simplify

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

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

sin (\frac{6}{8})

arccos (7)

3 sin (\frac{5 π}{6})

sin (28 0^{\circ})

10 \cdot sin (3 5^{\circ})

What is the value of sin((3pi)/(10))-sin(pi/(10)) ?
The value of sin((3pi)/(10))-sin(pi/(10)) is (sqrt(2)(1+sqrt(5))sqrt(3-\sqrt{5)})/8