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Answer 1 · 2017-03-02T15:50:26

see below

Use the formulas #cos x+cos y =2 cos (1/2 (x+y))cos(1/2(x-y))# and #cos(-x)=cosx#

Right Hand Side:
#1/2 [cosx+cos 3x]=1/2 [2cos (1/2 (x+3x))cos(1/2(x-3x))]#

#=1/cancel2 cancel2cos (1/2 (x+3x))cos(1/2(x-3x))#

#=cos (1/2 (4x))cos(1/2(-2x))#

#=cos 2x*cos(-x)#

#=cos2x cos x#

#=cosx cos 2x#

#:.=#Left Hand Side