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

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Answer 1 · 2016-06-28T23:45:15

$cos(pi/2) = 0$ so answer is zero. General case below.

Using Compound angle formulae:

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

Add these two together to get:

$1/2*(cos(A+B) + cos(A-B)) = cosAcosB$

So, $cos(pi/2)*cos((5pi)/12)$ can be written as:

$1/2*(cos(pi/2 + (5pi)/12) + cos(pi/2 - (5pi)/12))$

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