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Question

1sec2x+tan2xdx=log|sinx+f(x)|+C, then which of the following is/are correct?

A
fmin=0
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B
fmin=1
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C
fmax=2
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D
f(0)=1
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Solution

The correct option is D f(0)=1
cosx1+sin2xdxsinx=tcosx dx=dt=dt1+t2=logt+1+t2+C=logsinx+1+sin2x+C
f(x)=1+sin2x
So, fmin=1,fmax=2 and f(0)=1

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