The value of `x` satisfying the equation `cos^(-1)3x+sin^(-1)2x=pi` is

Options

A. `x=(1)/(sqrt(3))`
B. `x=(-1)/(sqrt(3))`
C. `x=(-1)/(sqrt(3))`
D. none of these

Answer

D

Explanation

`sin^(-1)2x=pi-cos^(-1)3x`
`rArr sin^(-1)2x=cos^(-1)(-3x)`
`rArr sqrt(1-4x^(2))=-3x(xlt 0)`
`rArr x^(2)=(1)/(13)`
`rArr x=(-1)/(sqrt(13))`
But for `x lt 0, pi//2 lt cos^(-1)3x lt pi` and `-pi//2 lt sin^(-1)2x lt 0`
`therefore L.H.S. ne pi`
Hence, equation has no solution.