If `f(x)={:{((cot x-cos x)/((pi-2x)^(3))", for " x != (pi)/(2)),(k ", for " x = pi/2):}` is continuous at `x

If `f(x)={:{((cot x-cos x)/((pi-2x)^(3))", for " x != (pi)/(2)),(k ", for " x = pi/2):}` is continuous at `x= pi/2`, where , then `k=`
A. `1/4`
B. `(1)/(24)`
C. `(1)/(16)`
D. `1/8`

If `f(x)={:{((cot x-cos x)/((pi-2x)^(3))", for " x != (pi)/(2)),(k ", for " x = pi/2):}` is continuous at `x= pi/2`, where , then `k=`

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