How do you express $cos (\frac{π}{2}) \cdot cos (\frac{5 π}{12})$ $cos(pi/ 2 ) * cos (( 5 pi) / 12 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{π}{2}) \cdot cos (\frac{5 π}{12})$ $cos(pi/ 2 ) * cos (( 5 pi) / 12 )$ without using products of trigonometric functions?

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Answer 1 · 2016-06-28T23:45:15

$cos (\frac{π}{2}) = 0$ $cos(pi/2) = 0$ so answer is zero. General case below.

Explanation:

Using Compound angle formulae:

$cos (A + B) = cos (A) cos (B) - sin (A) sin (B)$ $cos(A+B) = cos(A)cos(B) - sin(A)sin(B)$
$cos (A - B) = cos (A) cos (B) + sin (A) sin (B)$ $cos(A-B) = cos(A)cos(B) + sin(A)sin(B)$

Add these two together to get:

$\frac{1}{2} \cdot (cos (A + B) + cos (A - B)) = cos A cos B$ $1/2*(cos(A+B) + cos(A-B)) = cosAcosB$

So, $cos (\frac{π}{2}) \cdot cos (\frac{5 π}{12})$ $cos(pi/2)*cos((5pi)/12)$ can be written as:

$\frac{1}{2} \cdot (cos (\frac{π}{2} + \frac{5 π}{12}) + cos (\frac{π}{2} - \frac{5 π}{12}))$ $1/2*(cos(pi/2 + (5pi)/12) + cos(pi/2 - (5pi)/12))$

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How do you express $cos (\frac{π}{2}) \cdot cos (\frac{5 π}{12})$ $cos(pi/ 2 ) * cos (( 5 pi) / 12 )$ without using products of trigonometric functions?

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How do you express cos(π2)⋅cos(5π12)cos(pi/ 2 ) * cos (( 5 pi) / 12 ) without using products of trigonometric functions?

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How do you express $cos (\frac{π}{2}) \cdot cos (\frac{5 π}{12})$ $cos(pi/ 2 ) * cos (( 5 pi) / 12 )$ without using products of trigonometric functions?