How do you express cos( (15 pi)/ 8 ) * cos (( 5 pi) /12 ) without using products of trigonometric functions?

1 Answer
Jan 23, 2017

The answer is =1/2(cos(55/24pi)+cos(35/24pi))

Explanation:

cos(A+B)=cosAcosB-sinAsinB

cos(A-B)=cosAcosB+sinAsinB

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

Therefore,

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

Here,

A=15/8pi and B=5/12pi

So,

cos(15/8pi)cos(5/12pi)=1/2(cos(15/8pi+5/12pi))+cos(15/8pi-5/12pi))

=1/2(cos(55/24pi)+cos(35/24pi))