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Question

If f(x)=sin2x+sin2(x+π3)+cosxcos(x+π3) and g(54)=1, then find (gof)(x).

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Solution

f(x)=sinx+[12sinx+cosx×32]2+cos[12cosx32sinx]
f(x)=sinx+14[3cosx+sinx]2+12[cos2x3sinxcosx]
sin2x+34cos2x+sin2x4+32sinxcosx+cos2x232sinxcosx
54sin2x+54cos2x
54(sin2x+cos2x)
54f(x)=54
(gof)(x)=g(f(x))=g(54)=1

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