If# cosx/a_1=(cos2x)/a_2=(cos3x)/a_3# then show that #sin^2(x/2)=(2a_2-a_1-a_3)/(4a_2)#?

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Answer 1 · 2017-10-24T16:19:36

#RHS=(2a_2-a_1-a_3)/(4a_2)#

#=1/4(2-a_1/a_2-a_3/a_2)#

#=1/4(2-cosx/(cos2x)-(cos3x)/(cos2x))#

#=1/4(2-(cosx+cos3x)/(cos2x))#

#=1/4(2-(2cos2xcosx)/(cos2x))#

#=2/4(1-cosx)#

#=1/2xx2sin^2(x/2)#

#=sin^2(x/2)=LHS#