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The slope of tangent at a point (x,y) to...

The slope of tangent at a point `(x,y)` to the curve `y=f(x)` is equal to `2tanx (cosx-y)` , if the curve passes through point `(pi/4,0)` then the value of `int_0^(pi/2) f(x) dx`

A

`2-pi/sqrt2`

B

`2+pi/sqrt2`

C

`4-pi/sqrt2`

D

`4+pi/sqrt2`

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