limx→π/2 cotx - cosx/(π - 2x)3 is equal to

The correct option is B 116
limx→π/2 cotx - cosx/(π - 2x)3
Taking , (π/2 - x) = t
We get:
limx→π/2 cosx/sinx(1 - sinx) × 1/t3
Taking cotx = cosx/sinx for the above equation and taking cosx common.
Now,(sin(π/2 - t) = cost)
Hence, we get
limx→π/2 sint/cost(1 - cost) × 1/t3
limx→π/2 sint(2sin2t/2)/cost
Using L'Hospital rule
limx→π/2 1/2 × 2 × sint/t × 2sin2t/2/4(t2)2 × 1/cost
Hence we get:
1/2 × 8 = 1/16