Answer:
cos(Ļ/3)cos(Ļ/5) + sin(Ļ/3)sin(Ļ/5) = cos(2Ļ/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 ā sinAsinB
Cos (A ā B) = cosAcosB + sinAsinB
Sin (A + B) = sinAcosB + sinBcosA
Sin (A ā B) = sinAcosB ā sinBcosA
Given cos(Ļ/3)cos(Ļ/5) + sin(Ļ/3)sin(Ļ/5) if we let A = Ļ/3 and B = Ļ/5, it reduces to
cosAcosB + sinAsinB and we know that
cosAcosB + sinAsinB = cos(A ā B). Therefore,
cos(Ļ/3)cos(Ļ/5) + sin(Ļ/3)sin(Ļ/5) = cos(Ļ/3 ā Ļ/5) = cos(2Ļ/15)
