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If intsqrt(2+tan^(2)x)dx-ln tanx+sqrt(2+...

If `intsqrt(2+tan^(2)x)dx-ln tanx+sqrt(2+tan^(2)x)+f(x)+c`, then `f(x)=`

A

`sin^(-1)((sinx)/(sqrt2))`

B

`cos^(-1)((sinx)/(sqrt2))`

C

`cos^(-1)((cosx)/(sqrt2))`

D

`sin^(-1)((cosx)/(sqrt2))`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If intcos x log (tan""(x)/(2))dx=sin x log (tan""(x)/(2))+f(x) then f(x) is equal to, (assuming c is an arbitrary real constant)

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    strictly increases only in `(0,oo)`
    C
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    D
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