Answer:
cos(Ο/3)cos(Ο/5) + sin(Ο/3)sin(Ο/5) = cos(2Ο/15)
Step-by-step explanation:
We will make use of trig identities to solve this. Here are some common trig identities.
Cos (A + B) = cosAcosB β sinAsinB
Cos (A β B) = cosAcosB + sinAsinB
Sin (A + B) = sinAcosB + sinBcosA
Sin (A β B) = sinAcosB β sinBcosA
Given cos(Ο/3)cos(Ο/5) + sin(Ο/3)sin(Ο/5) if we let A = Ο/3 and B = Ο/5, it reduces to
cosAcosB + sinAsinB and we know that
cosAcosB + sinAsinB = cos(A β B). Therefore,
cos(Ο/3)cos(Ο/5) + sin(Ο/3)sin(Ο/5) = cos(Ο/3 β Ο/5) = cos(2Ο/15)
