How do you express $cos (\frac{π}{2}) \cdot cos (\frac{17 π}{12})$ $cos(pi/ 2 ) * cos (( 17 pi) / 12 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{π}{2}) \cdot cos (\frac{17 π}{12})$ $cos(pi/ 2 ) * cos (( 17 pi) / 12 )$ without using products of trigonometric functions?

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Answer 1 · 2016-01-05T00:42:36

$\frac{1}{2} (cos (\frac{23 π}{12}) + cos (\frac{- 11 π}{12}))$ $1/2(cos((23pi)/12)+cos((-11pi)/12))$

Explanation:

Use the rule:

$cos (a) cos (b) = \frac{1}{2} (cos (a + b) + cos (a - b))$ $cos(a)cos(b)=1/2(cos(a+b)+cos(a-b))$

Thus,

$cos (\frac{π}{2}) cos (\frac{17 π}{12}) = \frac{1}{2} (cos (\frac{π}{2} + \frac{17 π}{12}) + cos (\frac{π}{2} - \frac{17 π}{12}))$ $cos(pi/2)cos((17pi)/12)=1/2(cos(pi/2+(17pi)/12)+cos(pi/2-(17pi)/12))$

$= \frac{1}{2} (cos (\frac{23 π}{12}) + cos (\frac{- 11 π}{12}))$ $=1/2(cos((23pi)/12)+cos((-11pi)/12))$

This could continue to be simplified using half angle formulas, but this answer is fine as is given the parameters ("without using products of trigonometric functions").

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How do you express $cos (\frac{π}{2}) \cdot cos (\frac{17 π}{12})$ $cos(pi/ 2 ) * cos (( 17 pi) / 12 )$ without using products of trigonometric functions?

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Explanation:

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How do you express $cos (\frac{π}{2}) \cdot cos (\frac{17 π}{12})$ $cos(pi/ 2 ) * cos (( 17 pi) / 12 )$ without using products of trigonometric functions?