Question

How do you express `cos( (5 pi)/4 ) * cos (( 2 pi) /3 )` without using products of trigonometric functions?

Answer 1

`sqrt2/4`

Explanation:

`P = cos ((5pi)/4) .cos ((2pi)/3)`
Trig unit circle and trig table give -->
`cos ((5pi)/4) = cos (pi/4 + pi) = -cos (pi/4) = -sqrt2/2`
`cos ((2pi)/3) = cos (-pi/3 + pi) = - cos pi/3 = - 1/2`
`P = (-sqrt2/2)(-1/2) = sqrt2/4`