If `tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2)` then `x^(4)-x^(2)(Sigma ab)+abcd=`

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

B

Explanation

We have
`tan^(-1)(a)/(x)+tan^(-1)(b)/(x)+tan^(-1)(c )/(x)+tan^(-1)(d)/(x)=(pi)/(2)`
`rarr tan^(-1)(a)/(x)+tan^(-1)(b)/(x)=(pi)/(2)-{tan^(-1)(c )/(x)+tan^(-1)(d)/(x)}`
`rarr tan^(-1) ((a+b)x)/(x^(2)-ab)=(pi)/(2)-tan^(-1)((c+d)x)/(x^(2)-cd)`
`rarr tan^(-1)((a+b)x)/(x^(2)-ab)=co^(-1)((c+d)x)/(x^(2)-cd)`
`rarr tan^(-1)((a+b)x)/(x^(2)-ab)=(x^(2)-cd)/((c+d)x) rarr x^(4) -x^(2) (Sigma ab)+abcd=0`