Question

prove that cos2x + cos2 [ x+pie/3] + cos2 [x-pie/3] = 3/2

Answer 1

i think the question is incomplete or wrong.....correct me if i'm wrong thou


but let's solve the L.H.S first

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

so
cos2 [ x+pie/3] + cos2 [x-pie/3] = 2cos2xcos2[pie/3] = -cos2x (as cos(2pie/3) = -1/2)

so cos2x-cos2x = 0

so L.H.S  = 0