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

1 Answer
Jun 28, 2016

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)

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))