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Question

Let f(x)=sinx+cosx+tanx+arcsinx+arccosx+arctanx. If M and m are maximum and minimum values of f(x) then their arithmetic mean is equal to

A
π2+cos1
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B
π2+sin1
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C
π4+tan1+cos1
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D
π4+tan1+sin1
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Solution

The correct option is A π2+cos1
The domain of f(x) will be [1,1]
Hence
f(1)
=sin1+cos1tan1π2+ππ4
=m ...(i)
f(1)
=sin1+cos1+tan1+π2+0+π4
=M ...(ii)
Hence M+m
=2cos1+π
Thus mean will be
m+M2 =cos1+π2

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