How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{2 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{2 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?

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Answer 1 · 2016-05-14T05:14:30

$- (\frac{1}{2}) cos (\frac{π}{8})$ $-(1/2)cos (pi/8)$

Explanation:

$P = cos (\frac{15 π}{8}) cos (\frac{2 π}{3})$ $P = cos ((15pi)/8)cos ((2pi)/3)$
trig table gives -->cos (2pi)/3 = - 1/2
$cos (\frac{15 π}{8}) = cos (- \frac{π}{8} + \frac{16 π}{8}) = cos (- \frac{π}{8} + 2 π) =$ $cos ((15pi)/8) = cos (-pi/8 + (16pi)/8) = cos (-pi/8 + 2pi) =$
$= cos (- \frac{π}{8}) = cos (\frac{π}{8})$ $= cos (-pi/8) = cos (pi/8)$
Therefor, P can be expressed as:
$P = - (\frac{1}{2}) cos (\frac{π}{8})$ $P = -(1/2)cos (pi/8)$

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{2 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?

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Explanation:

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{2 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?