What is the value of sin(18)sin(54) ?

The value of sin(18)sin(54) is (sqrt(2)(sqrt(5)+1)sqrt(3-\sqrt{5)})/(16)

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sin(18)sin(54)

sin (1 8^{\circ}) sin (5 4^{\circ})

\frac{2 ( 5 + 1 ) 3 - 5}{16}

Solution steps

sin (1 8^{\circ}) sin (5 4^{\circ})

Rewrite using trig identities:

sin (5 4^{\circ}) = cos (3 6^{\circ})

= sin (1 8^{\circ}) cos (3 6^{\circ})

Rewrite using trig identities:

sin (1 8^{\circ}) = \frac{1 - cos ( 3 6 ^{\circ} )}{2}

= \frac{1 - cos ( 3 6 ^{\circ} )}{2} cos (3 6^{\circ})

Rewrite using trig identities:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

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

Simplify

\frac{1 - \frac{5 + 1}{4}}{2} \frac{5 + 1}{4} : \frac{2 ( 5 + 1 ) 3 - 5}{16}

= \frac{2 ( 5 + 1 ) 3 - 5}{16}

sin (\frac{31 π}{6})

arccos (\frac{2}{4})

arcsin (\frac{1}{2} - \frac{3}{5})

sin^{2} (3 π)

sin (9 2^{\circ})

What is the value of sin(18)sin(54) ?
The value of sin(18)sin(54) is (sqrt(2)(sqrt(5)+1)sqrt(3-\sqrt{5)})/(16)