Let x1,x2,x3,x4 be four non zero numbers...

Let `x_1,x_2,x_3,x_4` be four non zero numbers satisfying the equation `tan^-1 (a/x)+tan^-1(b/x)+tan^-1(c/x)+tan^-1(d/x)=pi/2` then which ofthe following relation(s) hold good?

A

`sum_(i=1)^(4)x_(i)=a+b+c+d`

B

`sum_(i=1)^(4)(1)/(x_(i))=0`

C

`prod_(i=1)^(4)x_(i)=abcd`

D

`(x_(1)+x_(2)+x_(3))(x_(2)+x_(3)+x_(4))(x_(3)+x_(4)+x_(1))(x_(4)+x_(1)+x_(2))=abcd`

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The correct Answer is:

B, C, D

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