How do you express $sin(pi/ 4 ) * sin( ( 5 pi) / 3 )$ without using products of trigonometric functions?

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Answer 1 · 2018-07-01T10:09:29

$color(violet)(=> (sin (pi/3) - sin (pi/6))/2$

https://lo.wikipedia.org/wiki/%E0%BB%84%E0%BA%95%E0%BA%A1%E0%BA%B8%E0%BA%A1

$sin A cos b = (1/2) (sin (A+B) + sin (A-B)), Identity$

$sin (pi/4) * sin ((5pi)/3)$

$=> (1/2) (sin (pi/4 + (5pi)/3) + sin (pi/4 - (5pi)/3))$

$=> (1/2) (sin ((8pi)/12) + sin -(pi/6))$

$=> (sin ((2pi)/3) - sin (pi/6))/2$

$color(violet)(=> (sin (pi/3) - sin (pi/6))/2$

How do you express sin(pi/ 4 ) * sin( ( 5 pi) / 3 ) sin(pi/ 4 ) * sin( ( 5 pi) / 3 ) without using products of trigonometric functions?