Convert 5cos(5π3)cos(5π3) as a sum of trigonometric ratios?

1 Answer
Mar 29, 2017

5cos(5π3)cos(5π3)=52(cos(10π3)+cos0)

= 52(cos(10π3)+1)

Explanation:

As cos(A+B)=cosAcosBsinAsinB and

cos(AB)=cosAcosB+sinAsinB

adding the two we get cos(A+B)+cos(AB)=2cosAcosB

Hence 5cos(5π3)cos(5π3)

=52×2cos(5π3)cos(5π3)

=52×(cos(5π3+5π3)+cos(5π35π3))

=52×(cos(10π3)+cos0), but cos0=1

Hence 5cos(5π3)cos(5π3)=52×(cos(10π3)+1)