If f(x)=sin2x + sin2(x+pi/3)+ cosx*cos(x+pi/3), and g(5/4)=1 then find gof(x)

Dear student

We have,f(x)=sin2x+sin2x+π3+cosx cosx+π3f(x)=122sin2x+2sin2x+π3+2cosx cosx+π3f(x)=121-cos2x+1-cos2x+2π3+cos2x+π3+cosπ3f(x)=1252-cos2x-cos2x+2π3+cos2x+π3f(x)=1252-cos2x+cos2x+2π3+cos2x+π3f(x)=1252-2cos2x+π3cosπ3+cos2x+π3f(x)=1252-cos2x+π3+cos2x+π3f(x)=54 for all xRTherefore, for any xR, we havegof(x)=gfx=g54=1Thus, gof(x)=1 for all xRHence, gof:RR is a constant function. 
Regards

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