Question

How do you express `cos( (5 pi)/4 ) * cos (( 5 pi) /3 )` without using products of trigonometric functions?

Answer 1

`-sqrt2/4`

Explanation:

`cos ((5pi)/4) = cos (pi/4 + pi) = - cos pi/4 = -sqrt2/2`
`cos ((5pi)/3) = cos ((2pi)/3 + pi) = - cos ((2pi)/3) = 1/2`

Product `cos((5pi)/4)cos ((5pi)/3) = -(sqrt2/2)(1/2) = -sqrt2/4`