Evaluate `lim_(xto pi//4) (1-cot^(3)x)/(2-cotx-cot^(3)x).`

Answer

`3//4`

Explanation

`underset(xto pi//4)lim(1-cot^(3)x)/(2-cotx-cot^(3)x)`
`=underset(xto(pi)/(4))lim((1-cotx))/((1-cotx))((1+cotx+cot^(2)x))/((cot^(2)x+cotx+2))`
`=(1+1+1)/(2+1+1)=3/4`