How do you express $sin (\frac{π}{12}) \cdot cos (\frac{17 π}{12})$ $sin(pi/12) * cos(( 17 pi)/12 )$ without products of trigonometric functions?

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{17 π}{12})$ $sin(pi/12) * cos(( 17 pi)/12 )$ without products of trigonometric functions?

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Answer 1 · 2016-03-15T14:06:26

$P = - {sin}^{2} (\frac{π}{12})$ $P = - sin^2 (pi/12)$

Explanation:

$P = sin (\frac{π}{12}) . cos (\frac{17 π}{12}) .$ $P = sin (pi/12).cos ((17pi)/12).$
First, find $cos (\frac{17 π}{12})$ $cos ((17pi)/12)$
$cos (\frac{17 π}{12}) = cos (\frac{5 π}{12} + π) = - cos (\frac{5 π}{12})$ $cos ((17pi)/12) = cos ((5pi)/12 + pi) = - cos ((5pi)/12)$ (supplementary)
$cos (\frac{5 π}{12}) = cos (\frac{π}{2} - \frac{π}{12}) = sin (\frac{π}{12})$ $cos ((5pi)/12) = cos (pi/2 - pi/12) = sin (pi/12)$ . (complementary arcs)
The product reduces to
$P = - {sin}^{2} (\frac{π}{12})$ $P = - sin^2 (pi/12)$

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{17 π}{12})$ $sin(pi/12) * cos(( 17 pi)/12 )$ without products of trigonometric functions?

1 Answer

Explanation:

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How do you express sin(π12)⋅cos(17π12)sin(pi/12) * cos(( 17 pi)/12 ) without products of trigonometric functions?

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{17 π}{12})$ $sin(pi/12) * cos(( 17 pi)/12 )$ without products of trigonometric functions?