यदि x, y, z एक समान्तर श्रेढी में है तथा `tan^(-1)x, tan^(-1)y` तथा `tan^(-1)(z)` भी समान्तर श्रेढी में है, तो-

Options

A. `x = y = z`
B. `2x = 3y = 6z`
C. `6x = 3y = 2z`
D. `6x = 4y = 3z`

Answer

A

Explanation

`2y = x + z`
`2tan^(-1)y = tan^(-1)x + tan^(-1)(z)`
`tan^(-1)((2y)/(1-xz)) = tan^(-1)((x + z)/(1-xz))`
`(x + z)/(1-y^(2)) = (x + z)/(1-xz)`
`rArr y^(2) = xz` & `x + z =0`
`rArr x = y = z`