Question

In a triangle $ABC$ right angled at C, $\tan A$ and $\tan B$ satisfy the equation

• A. $ab{x}^2-(a^2+b^2)x-ab=0$
• B. $ab{x}^2-c^{2}x+ab=0$
• C. $c^2{x}^2-abx+c^2=0$
• D. $a{x}^2-bx+a=0$

Answer 1

The correct option is B $ab{x}^2-c^{2}x+ab=0$

$p{x}^2+qx+s=0$
$ab{x}^2-c^{2}x+ab=0\to 1$
$\tan A=\frac{a}{b}\tan B=\frac{b}{a}$
$\tan A.\tan b=\frac{ab}{ab}=1=\frac{5}{q}=\frac{ab}{ab}$
$\tan A+\tan b=\frac{a}{b}+\frac{b}{a}=\frac{a^2+b^2}{ab}=\frac{c^2}{ab}=\frac{-q}{p}$
$\therefore$By using properties of quadratic equation, we can clearly see $\tan A$ & $\tan B$ satisfy the equation.