1.

If `m` and `x` are real numbers where `m in I` `e^(2micot^(-1)x)((x.i+1)^m)/((x.i-1)^m)`

Answer» `Cot^(-1)x=theta`
`x=cottheta`
`((x i+1)/(x i-1))^m=(i^n(x+1/i)^m)/(i^m(x-1/i)^m)`
`=(x-1)^m/(x+i)^n`
`=(cottheta-1)^m/(cottheta+1)^m`
`=(costheta-sintheta)^m/(costheta+sintheta)^m`
`=(e^(-itheta)/e^(1theta))=(e^(-i2theta))^m`
`=e^(i2mtheta)`
`=e^(i2mtheta-i2mtheta)=e^0=1`
option c is correct.


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