What will be the solution of the mentioned problem?

prove that,cosnAcos(n+2)A-cos^2(n+1)A+sin^2A=0

1 Answer
Dec 20, 2017

LHS=cosnAcos(n+2)A-cos^2(n+1)A+sin^2A

=cosnAcos(n+2)A-1/2(1+cos2(n+1)A)+1/2(1-cos2A)
=cosnAcos(n+2)A-1/2cos2(n+1)A-1/2cos2A

=cosnAcos(n+2)A-1/2(cos2(n+1)A+cos2A)

=cosnAcos(n+2)A-1/2(2cos(n+2)AcosnA)

=cosnAcos(n+2)A-cos(n+2)AcosnA

=0=RHS