Question

The number of real solution of the equation $ta{n}^{-1}\sqrt{x^2-3x+2}+co{s}^{-1}\sqrt{4x-x^2-3}=\pi$ is

• A. 1
• B. 2
• C. 0
• D. infinite

Answer 1

Answer: (C)

0

Consider a function
$f\left(x\right)=ta{n}^{-1}\left(\sqrt{x^2-3x+2}\right)+co{s}^{-1}\left(\sqrt{4x-x^2-3}\right)-\pi$
For $f\left(x\right)$ to be zero, its graph must cut the x axis at some point $x_1$
However, we can see from its graph, that it does not cut the x axis at any point.
Hence there is no solution for the equation
$ta{n}^{-1}\left(\sqrt{x^2-3x+2}\right)+co{s}^{-1}\left(\sqrt{4x-x^2-3}\right)=\pi$