How do you express cos(π2)cos(5π12) without using products of trigonometric functions?

1 Answer
Jun 28, 2016

cos(π2)=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(AB)=cos(A)cos(B)+sin(A)sin(B)

Add these two together to get:

12(cos(A+B)+cos(AB))=cosAcosB

So, cos(π2)cos(5π12) can be written as:

12(cos(π2+5π12)+cos(π25π12))