Question

If `-1lexle0` then `sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x^(2)))}` is equal to
A. 1
B. `-1`
C. 0
D. none of these

Answer 1

We know that `tan^(-1)=-pi+cot^(-1)(1/x)if xlt0`
`therefore {tan^(-1)(1-x^(2))/(2x) -cosf^(-1)(1-x^(2))/(1+x^(2))}`
`=sin{-pi+co^(-1)(2x)/(1-x^(2))-cos^(-1)(1-x^(2))/(1+x^(2))}`
`=sin{-(pi)/(2)-2tn^(-2)tan^(-1)x+2tan^(-1)x+2tan^(-1)x}`
`=sin(-(pi)/(2))=-1`