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
P dilip_k
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#

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