The number of real values of x satisfying `tan^-1(x/(1-x^2))+tan^-1 (1/x^3)` =`(3pi)/(4)`

Options

A. A. 0
B. B. 1
C. C. 2
D. D. Infinitely many

Answer

no solution

Explanation

Given equation is `tan^(-1) ((x)/(1 -x^(2))) + tan^(-1) ((1)/(x^(3))) = (3pi)/(4)`
Clearly `x != +- 1`
`tan^(-1) ((x)/(1 - x^(2))) + tan^(-1) ((1)/(x^(3))) = tan.((x)/(1 - x^(2)) + (1)/(x^(3)))/(1 - (x)/(x^(3) (1 - x^(2))))`
`= tan^(-1).(x^(4) + 1 -x^(2))/((x^(2) -x^(4) -1) x)`
`= tan^(-1).(-(1)/(x))`
`:. tan^(-1) (-(1)/(x)) = (3pi)/(4)`
`rArr x = 1, " but " x != 1`
So the given equation has no solution