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

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

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Answer 1 · 2016-12-21T14:27:21

$(\frac{1}{2}) [sin (\frac{π}{24}) + (\frac{1}{2}) sin (\frac{5 π}{24})]$ $(1/2)[sin (pi/24) + (1/2)sin ((5pi)/24)]$

Explanation:

$P = sin (\frac{π}{12}) . cos (\frac{π}{8})$ $P = sin (pi/12).cos (pi/8)$
Use trig identity:
$sin a . cos b = (\frac{1}{2}) [sin (a - b) + (\frac{1}{2}) (sin (a + b)]$ $sin a.cos b = (1/2)[sin (a - b) + (1/2)(sin (a + b)]$
We have:
$sin (a - b) = sin ((\frac{π}{8}) - (\frac{π}{12})) = sin (\frac{π}{24})$ $sin (a - b) = sin ((pi/8) - (pi/12)) = sin (pi/24)$
$sin (a + b) = sin ((\frac{π}{8}) + (\frac{π}{12})) = sin (\frac{5 π}{24})$ $sin (a + b) = sin ((pi/8) + (pi/12)) = sin ((5pi)/24)$
There for, P can be expressed as:
$P = (\frac{1}{2}) [sin (\frac{π}{24}) + (\frac{1}{2}) sin (\frac{5 π}{24})]$ $P = (1/2)[sin (pi/24) + (1/2)sin ((5pi)/24)]$

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

1 Answer

Explanation:

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

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