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How to prove that #cos^2((4pi)/7)-sin^2((3pi)/7)=cos((6pi)/7)#?

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May 28, 2018

#LHS=cos^2((4pi)/7)-sin^2((3pi)/7)#

#=cos^2((4pi)/7)-sin^2(pi-(4pi)/7)#
#=cos^2((4pi)/7)-sin^2((4pi)/7)#

#=cos((8pi)/7)#

#=cos(2pi-(6pi)/7)#

#=cos((6pi)/7)=RHS#

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