Question

If $\tan x.\tan y=a$ and $x+y=\frac{Ï€}{6},$ then tan $x$ and $\tan y$ satisfy the equation

• A. $x^2−\sqrt{3}(1−a)x+a=0$
• B. $\sqrt{3}{x}^2−(1−a)x+a\sqrt{3}=0$
• C. $x^2+\sqrt{3}(1+a)x−a=0$
• D. $\sqrt{3}{x}^2+(1+a)x−a\sqrt{3}=0$

Answer 1

Answer: (B)

$âˆ\mu \tan xâ‹\dots \tan y=a$
and $\tan (x+y)=\tan \left(\frac{Ï€}{6}\right)$
$⇒\frac{\tan x+\tan y}{1−\tan xâ‹\dots \tan y}=\frac{1}{\sqrt{3}}$
$⇒\tan x+\tan y=\frac{1}{\sqrt{3}}(1−a)$
Equation whose roots are tan $x$ and tan $y$ is
$x^2−\frac{(1−a)}{\sqrt{3}}â‹\dots x+a=0$
$⇒\sqrt{3}{x}^2−(1−a)x+a\sqrt{3}=0$