How do you express $sin (\frac{π}{4}) \cdot sin (\frac{5 π}{3})$ $sin(pi/ 4 ) * sin( ( 5 pi) / 3 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{5 π}{3})$ $sin(pi/ 4 ) * sin( ( 5 pi) / 3 )$ without using products of trigonometric functions?

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Answer 1 · 2018-07-01T10:09:29

$\Rightarrow \frac{sin (\frac{π}{3}) - sin (\frac{π}{6})}{2}$ $color(violet)(=> (sin (pi/3) - sin (pi/6))/2$

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$sin A cos b = (\frac{1}{2}) (sin (A + B) + sin (A - B)), I d e n t i t y$ $sin A cos b = (1/2) (sin (A+B) + sin (A-B)), Identity$

$sin (\frac{π}{4}) \cdot sin (\frac{5 π}{3})$ $sin (pi/4) * sin ((5pi)/3)$

$\Rightarrow (\frac{1}{2}) (sin (\frac{π}{4} + \frac{5 π}{3}) + sin (\frac{π}{4} - \frac{5 π}{3}))$ $=> (1/2) (sin (pi/4 + (5pi)/3) + sin (pi/4 - (5pi)/3))$

$\Rightarrow (\frac{1}{2}) (sin (\frac{8 π}{12}) + sin - (\frac{π}{6}))$ $=> (1/2) (sin ((8pi)/12) + sin -(pi/6))$

$\Rightarrow \frac{sin (\frac{2 π}{3}) - sin (\frac{π}{6})}{2}$ $=> (sin ((2pi)/3) - sin (pi/6))/2$

$\Rightarrow \frac{sin (\frac{π}{3}) - sin (\frac{π}{6})}{2}$ $color(violet)(=> (sin (pi/3) - sin (pi/6))/2$

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{5 π}{3})$ $sin(pi/ 4 ) * sin( ( 5 pi) / 3 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{5 π}{3})$ $sin(pi/ 4 ) * sin( ( 5 pi) / 3 )$ without using products of trigonometric functions?