Question

If $\tan x\times \tan y=a$ and $x+y=\frac{\pi }{6}$, then $\tan x$ and $\tan y$ satisfy the equation

• A. $x^2-\sqrt{2}(1-a)x+a=0$
• 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)

$\sqrt{3}{x}^2-(1-a)x+a\sqrt{3}=0$

If $\tan x\tan y$$=a$ and $x+y=\frac{\pi }{6}$
$\tan \frac{\pi }{6}=\tan (x+y)$
$=\frac{\tan x+\tan y}{1-a}$
$\Rightarrow \frac{1-a}{\sqrt{3}}=\tan x+\tan y$
So x & y satisfy the equation $\sqrt{3}{x}^2-(1-a)x+a\sqrt{3}=0$