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The number of real solution of the equat...

The number of real solution of the equation `tan^(-1) sqrt(x^(2) - 3x + 2) + cos^(-1) sqrt(4x - x^(2) -3) = pi` is

A

one

B

two

C

zero

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
Since `sqrt(x^(2) - 3x + 2) ge 0`
`rArr 0 le tan^(-1) sqrt(x^(2) - 3x + 2) lt (pi)/(2)`
and `sqrt(4x -x^(2) -3) le 0 rArr 0 lt cos^(-1) sqrt(4x - x^(2) -3) le (pi)/(2)`
Adding, we have `0 lt L.H.S. lt pi`
Therefore, the given equation has no solution
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