If f(x) is continuous at x=pi/2, where ...

If `f(x)` is continuous at `x=pi/2`, where `f(x)=(sqrt(2)-sqrt(1+sin x))/(cos^(2)x)`, for `x!= pi/2`, then `f(pi/2)=`

A

(a) `1/(sqrt2)`

B

(b) `1/(2sqrt2)`

C

(c) `1/(3sqrt2)`

D

(d) `1/(4sqrt2)`

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The correct Answer is:

D

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