Question

In $△ABC$, if $\tan \frac{A}{2}$ and $\tan \frac{A}{2}$ are the roots of the equation $6x^2-5x+1=0$, then

• A. $a^2+b^2>c^2$
• B. $a^2-b^2=c^2$
• C. $a^2+b^2=c^2$
• D. None of these

Answer 1

The correct option is C $a^2+b^2=c^2$

If tan A/2 and tan B/2 are the roots of the eqn $6x^2-5x+1=0$, Then

$tanA/2+tanB/2=5/6tanA/2.tanB/2=1/6$

$\Rightarrow tan(A/2+B/2)=\frac{tanA/2+tanB/2}{1-tanA/2.tanB/2}=\frac{5/6}{1-1/6}=1$

$\therefore \frac{A}{2}+\frac{B}{2}=\frac{\pi }{4}$

$A+B=\frac{\pi }{2}$

$\angle C=\frac{\pi }{2}$

$\therefore △ABC$ is right angle triangle

$c^2=a^2+b^2$