If f(x)=sin^2 x+sin^2 (x+pi/3) +cos x cos(x+pi/3) and g(5/4)=1, then gof(pi/8) =?

Answers (1)

Solution:   We have ,

                    f(x)=sin^2x+sin^2(x+fracpi3)+cos x cos(x+fracpi3)

       Rightarrow      f(x)=frac12(1-cos 2x)+frac12[1-cos(2x+frac2pi3)]+frac12[cos(2x+fracpi3)+cos fracpi3]

       Rightarrow     f(x)=frac54-frac12[cos 2x+cos (2x+frac2pi3)-cos(2x+fracpi3)]

              f(x)=frac54-frac12[2cos(2x+fracpi3)cosfracpi3-cos(2x+fracpi3)]

        	herefore                     f(x)=frac54.      forall   x.

    Hence ,     f(fracpi8)=frac54   and   therefore   gof(fracpi8)=g(frac54)=1

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