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The lim(xto(pi)/2)(cot x-cosx)/((pi-2x)^...

The `lim_(xto(pi)/2)(cot x-cosx)/((pi-2x)^(3))` equals

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The correct Answer is:
C
`underset(xto(pi)/(2))lim(cotx-cosx)/((pi-2x)^(3))=underset(xto(pi)/(2))lim(cotx(1-sinx))/(8((pi)/(2)-x))`
`=(1)/(8)underset(xto(pi)/(2))lim(tan((pi)/(2)-x))/(((pi)/(2)-x)).((1-sin^(2)x))/(((pi)/(2)-x)^(2)).(1)/(1+sinx)`
`=(1)/(8)underset(xto(pi)/(2))lim(tan((pi)/(2)-x))/(((pi)/(2)-x)).(cos^(2)x)/(((pi)/(2)-x)^(2)).(1)/(1+sinx)`
`=(1)/(8)underset(xto(pi)/(2))lim(tan((pi)/(2)-x))/(((pi)/(2)-x)).(sin^(2)((pi)/(2)-x))/(((pi)/(2)-x)^(2)).(1)/(1+sinx)`
`=(1)/(8).1.1.(1)/(2)=(1)/(16)`
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