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

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

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sin(pi/(10))cos(pi/(10))

sin (\frac{π}{10}) cos (\frac{π}{10})

\frac{2 5 - 5}{8}

Solution steps

sin (\frac{π}{10}) cos (\frac{π}{10})

Rewrite using trig identities:

\frac{sin ( \frac{π}{5} )}{2}

= \frac{sin ( \frac{π}{5} )}{2}

Rewrite using trig identities:

sin (\frac{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}

sin (6 0^{\circ}) cos (3 0^{\circ}) + sin (3 0^{\circ}) cos (6 0^{\circ})

arccos (\frac{1}{15})

sin (18 0^{\circ}) + cos (18 0^{\circ})

sec (\frac{π}{4}) - \frac{1}{( \frac{π}{4} ) ^{3}} + 5

tan (- \frac{17 π}{4})

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