How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?

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How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?

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Answer 1 · 2016-03-25T12:09:01

$- {sin}^{2} (\frac{π}{8})$ $- sin^2 (pi/8)$

Explanation:

Trig unit circle and the property of complementary arcs give -->
$cos (\frac{5 π}{8}) = cos (\frac{π}{8} + \frac{4 π}{8}) = cos (\frac{π}{8} + \frac{π}{2}) = - sin (\frac{π}{8})$ $cos ((5pi)/8) = cos (pi/8 + (4pi)/8) = cos (pi/8 + pi/2) = - sin (pi/8)$
Therefor, the product can be expressed as:
$P = sin (\frac{π}{8}) . cos (\frac{5 π}{8}) = - {sin}^{2} (\frac{π}{8})$ $P = sin (pi/8).cos ((5pi)/8) = - sin^2 (pi/8)$

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How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?

1 Answer

Explanation:

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How do you express sin(π8)⋅cos(5π8)sin(pi/ 8 ) * cos(( 5 pi)/8 ) without products of trigonometric functions?

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Explanation:

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How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?