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Question

Let f(x)=4x+8cosx4ln{cosx(1+sinx)}+tanx2secx6. If f(x) is strictly increasing x(0,a) then

A
a=π6
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B
a=π3
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C
a=π2
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D
None of these
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Solution

The correct option is A a=π6
f(x)=48sinx4sinx+cos2xsin2xcosx(1+sinx)+sec2xsecxtanx=4(12sinx)4secx(12sinx)+sec2x(12sinx)f(x)=(secx2)2(12sinx)
If f(x)>0 x(0,a) then f(x) is increasing in (0,a)a=π6

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