Question

prove that cos6A=32cos^6A-48cos^4A+18cos^2A-1

Answer 1

LHS=COS 6X

∵COS 2X =2 COS²X-1

⇒COS 6X=COS 2(3X)

                =2×COS 3X²-1

                =2(4 COS³X-3 COSX)²-1

                =2(16 COS^6+9 COS²-24 COS^4X)-1

                =32 COS^6-48 COS^4+18 COS²X -1 RHS