Question

How do you express `cos(pi/ 2 ) * cos (( 17 pi) / 12 )` without using products of trigonometric functions?

Answer 1

`1/2(cos((23pi)/12)+cos((-11pi)/12))`

Explanation:

Use the rule:

`cos(a)cos(b)=1/2(cos(a+b)+cos(a-b))`

Thus,

`cos(pi/2)cos((17pi)/12)=1/2(cos(pi/2+(17pi)/12)+cos(pi/2-(17pi)/12))`

`=1/2(cos((23pi)/12)+cos((-11pi)/12))`

This could continue to be simplified using half angle formulas, but this answer is fine as is given the parameters ("without using products of trigonometric functions").