How do you express $sin (\frac{π}{4}) \cdot sin (\frac{2 π}{3})$ $sin(pi/ 4 ) * sin( ( 2 pi) / 3 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{2 π}{3})$ $sin(pi/ 4 ) * sin( ( 2 pi) / 3 )$ without using products of trigonometric functions?

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Answer 1 · 2018-07-03T09:05:38

$\Rightarrow \frac{cos (\frac{5 π}{12}) - cos (\frac{11 π}{12})}{2}$ $color(red)(=> [cos ((5pi)/12) - cos ((11pi)/12)]/2$

Explanation:

https://study.com/academy/lesson/product-to-sum-identities-uses-applications.html

$sin (\frac{π}{4}) \cdot sin (\frac{2 π}{3})$ $sin (pi/4) * sin ((2pi)/3)$

$sin x sin y = (\frac{1}{2}) [cos (x - y) - cos (x + y])$ $sin x sin y = (1/2)[cos(x-y) - cos (x+y])$

$\Rightarrow (\frac{1}{2}) [cos (\frac{π}{4} - \frac{2 π}{3}) - cos (\frac{π}{4} + \frac{2 π}{3})]$ $=> (1/2)[cos (pi/4 - (2pi)/3) - cos (pi/4 + (2pi)/3)]$

$\Rightarrow \frac{cos - (\frac{5 π}{12}) - cos (\frac{11 π}{12})}{2}$ $=> [cos -((5pi)/12) - cos ((11pi)/12)]/2$

$\Rightarrow \frac{cos (\frac{5 π}{12}) - cos (\frac{11 π}{12})}{2}$ $color(red)(=> [cos ((5pi)/12) - cos ((11pi)/12)]/2$

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{2 π}{3})$ $sin(pi/ 4 ) * sin( ( 2 pi) / 3 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{2 π}{3})$ $sin(pi/ 4 ) * sin( ( 2 pi) / 3 )$ without using products of trigonometric functions?