Question

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

Answer 1

`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))`