Question

How do you express `cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 )` without using products of trigonometric functions?

Answer 1

`1/2+1/2cos(pi/4)`

Explanation:

`cos((15pi)/8)*cos((15pi)/8)=cos^2((15pi)/8)`

As `cos2A=2cos^2A-1`, `cos^2A=1/2+(cos2A)/2`

Hence `cos((15pi)/8)*cos((15pi)/8)=1/2+1/2cos((15pi)/4)`

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

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