Question

If `-1lexle0` then `tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-x^(2))/(1+x^(2)))}` is equal to
A. `(2x)/(1-x^(2))`
B. 0
C. `(2x)/(1+x^(2))`
D. x

Answer 1

We know that
`sin^(-1)(2x)/(1+x^(2))=-2 tan^(-1) x if -1 le x le 1`
and
` cos^(-1)((1-x^(2))/(1+x^(2)))=-2 tan^(-1)x if -oo lex le 0`
`therefore tan{1/2sin^(-1)(2x)/(1+x^(2))+1/2 cos^(-1)(1-x^(2))/(1+x^(2)`
`=tan(tan^(-1)x-tan^(-1)x) if -1 le x le 0 =-tan 0=0`