How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{7 π}{4})$ $sin(pi/ 8 ) * cos(( ( 7 pi) / 4 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{7 π}{4})$ $sin(pi/ 8 ) * cos(( ( 7 pi) / 4 )$ without using products of trigonometric functions?

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Answer 1 · 2016-03-20T13:35:46

$P = (\frac{\sqrt{2}}{2}) sin (\frac{π}{8})$ $P = (sqrt2/2)sin (pi/8)$

Explanation:

$P = sin (\frac{π}{8}) cos (\frac{7 π}{4})$ $P = sin (pi/8)cos ((7pi)/4)$
$cos (\frac{7 π}{4}) = cos (- \frac{π}{4} + 2 π) = cos (- \frac{π}{4}) = \frac{cos π}{4} = \frac{\sqrt{2}}{2}$ $cos ((7pi)/4) = cos (-pi/4 + 2pi)= cos (-pi/4) = cos pi/4 = sqrt2/2$
P can be expressed as:
$P = (\frac{\sqrt{2}}{2}) sin (\frac{π}{8})$ $P = (sqrt2/2)sin (pi/8)$
We can find P by evaluating #sin (pi/8), if being asked.

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{7 π}{4})$ $sin(pi/ 8 ) * cos(( ( 7 pi) / 4 )$ without using products of trigonometric functions?

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Explanation:

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{7 π}{4})$ $sin(pi/ 8 ) * cos(( ( 7 pi) / 4 )$ without using products of trigonometric functions?