How do you express $sin (\frac{π}{12}) \cdot cos (\frac{13 π}{8})$ $sin(pi/12) * cos(( 13 pi)/8 )$ without products of trigonometric functions?

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{13 π}{8})$ $sin(pi/12) * cos(( 13 pi)/8 )$ without products of trigonometric functions?

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Answer 1 · 2016-03-31T04:34:25

sin (pi/8).sin (pi/12)

Explanation:

$P = sin (\frac{π}{8}) . cos (\frac{13 π}{8})$ $P = sin (pi/8).cos ((13pi)/8)$
Trig unit circle, properties of supplementary and complementary arcs give -->
$cos (\frac{13 π}{8}) = cos (\frac{5 π}{8} + π)) = - cos (\frac{5 π}{8}) =$ $cos ((13pi)/8) = cos ((5pi)/8 + pi)) = - cos ((5pi)/8) =$
$= - cos (\frac{π}{8} + \frac{π}{2}) = sin (\frac{π}{8}) .$ $= - cos (pi/8 + pi/2) = sin (pi/8).$
Therefor,
$P = sin (\frac{π}{12}) . sin (\frac{π}{8})$ $P = sin (pi/12).sin (pi/8)$

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{13 π}{8})$ $sin(pi/12) * cos(( 13 pi)/8 )$ without products of trigonometric functions?

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How do you express sin(pi/12) * cos(( 13 pi)/8 ) sin(π12)⋅cos(13π8)sin(pi/12) * cos(( 13 pi)/8 ) without products of trigonometric functions?

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{13 π}{8})$ $sin(pi/12) * cos(( 13 pi)/8 )$ without products of trigonometric functions?