We are given the following equation:
[tex]cot^2(\frac{\pi}{2}x)=3[/tex]To solve for "x" we will take the square root to both sides:
[tex]cot(\frac{\pi}{2}x)=\sqrt{3}[/tex]Now, we take the inverse function of cotangent:
[tex]\frac{\pi}{2}x=cot^{-1}\sqrt{2}[/tex]Solving the operations:
[tex]\frac{\pi}{2}x=\frac{\pi}{6}[/tex]Now, we can cancel out the pi:
[tex]\frac{1}{2}x=\frac{1}{6}[/tex]Now, we multiply both sides by 2:
[tex]x=\frac{2}{6}[/tex]Simplifying:
[tex]x=\frac{1}{3}[/tex]Therefore, the value of "x" is 1/3
