If the function f(x)={{:(,-x,x lt 1),(...

If the function
`f(x)={{:(,-x,x lt 1),(,a+cos^(-1)(x+b),1 le xle 2):}` is differentiable at x=1, then `(a)/(b)` is equal to

A

`(pi + 2)/(2)`

B

`(pi-2)/(2)`

C

`(-pi-2)/(2)`

D

`-1-cos^(-1)(2)`

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The correct Answer is:

A

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