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Question

If f(x)=sin2x+sin2x+π3+cosxcosx+π3 and g54=1, then gof(x) is equal to


A

1

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B

-1

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C

2

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D

-2

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Solution

The correct option is A

1


Explanation for the correct option.

Given, f(x)=sin2x+sin2x+π3+cosxcosx+π3 and g54=1.

f(x)=sin2x+sin2x+π3+cosx·cosx+π3=122sin2x+2sin2x+π3+2·cosx·cosx+π3=121-cos2x+1-cos2x+2π3+cos2x+π3+cosπ3[2·cosa·cosb=cos(a+b)+cos(a-b)&&2sin2x=1-cos2x]=1252-cos2x-cos2x+2π3+cos2x+π3=1252-2cos2x+π3cosπ3+cos2x+π3=1252-cos2x+π3+cos2x+π3=54

f(x)=54

Now, find gof(x).

gof(x)=g(f(x))=g54=1[Given:g(54)=1]

Hence, the correct option is A.


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