Q)Prove that: (2cosA+1)(2cosA-1)(2cos2A-1)= 2cos4A+1 R.H.S: =2cos4A+1
=2cos2*2A+1
=2(2cos^2 2A-1)+1 [becoz cos2A=2cos^2 A-1]
=4cos^2 2A-2+1
=4cos^2 2A-1
=(2cos2A)^2-(1)^2
=(2cos2A+1)(2cos2A-1) [becoz a^2-b^2=(a+b)(a-b) ]
={2(2cos^2 A-1)+1} (2cos2A-1)
=(4cos^2 A-2+1} (2cos2A-1)
=(4cos^2 A-1) (2cos2A-1)
={(2cosA)^2-(1)^2} (2cos2A-1)
=(2cosA+1)(2cosA-1)(2cos2A-1)
=L.H.S proved ##