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If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+p...

If `f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4)=1,` then `(gof)(x)` is ____________

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The correct Answer is:
1
`f(x)=sin^(2)x+sin^(2)(x+(pi)/(3))+cosxcos(x+(pi)/(3))`
`=sin^(2)x+(1)/(4)(sinx+sqrt(3)cosx)^(2)+(1)/(2)cosx(cosx-sqrt(3)sinx)`
`=(5)/(4)(sin^(2)x+cos^(2)x)=(5)/(4)`
`(gof)x=g[f(x)]=g(5//4)=1`
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