Question

Find the value of $\tan (A+B)$ if the roots of the equation $6x^2-5x+1=0$ are $\tan A$ and $\tan B$

Answer 1

Sin $\tan A$ and $\tan B$ are the roots of $6x^2-5x+1=0$.
Now, using the relation between roots and coefficients of a quadratic equation, we have
$\tan A+\tan B=\frac{5}{6}$
$\tan A\tan B=\frac{1}{6}$

Since $\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

$=\frac{\frac{5}{6}}{1-\frac{1}{6}}=\frac{\frac{5}{6}}{\frac{5}{6}}=1$