How do you verify the identity #cos(pi/3+x)+cos(pi/3-x)=cosx#?

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Answer 1 · 2017-10-07T08:22:35

Please refer to a Proof in the Explanation.

Using, #cosC+cosD=cos((C+D)/2)cos((C-D)/2),# we have,

#cos(pi/3+x)+cos(pi/3-x),#

#=2cos(1/2){(pi/3+x)+(pi/3-x))}cos(1/2){(pi/3+x)-(pi/3-x)},#

#=2cos(pi/3)cosx,#

#=2*1/2*cosx,#

#=cosx.#

Hence, the Proof.