How do you express cos( (15 pi)/ 8 ) * cos (( 5 pi) /8 ) without using products of trigonometric functions?

1 Answer
Apr 4, 2016

cos((15pi)/8)cos ((5pi)/8)=1/2 cos((5pi)/2)+1/2 cos((5pi)/4)=-sqrt2/2

Explanation:

2cos A cos B=cos(A+B)+cos(A-B)

cosAcos B=1/2 (cos(A+B)+cos(A-B))

A=(15pi)/8, B=(5pi)/8

=>cos((15pi)/8)cos ((5pi)/8)=1/2 (cos((15pi)/8+(5pi)/8)+cos((15pi)/8-(5pi)/8))

=1/2 (cos((20pi)/8)+cos((10pi)/8))

=1/2 cos((5pi)/2)+1/2 cos((5pi)/4) =0+ -sqrt2/2=-sqrt2/2

cos((15pi)/8)cos ((5pi)/8)=1/2 cos((5pi)/2)+1/2 cos((5pi)/4)=-sqrt2/2