Question

If $\tan A,\tan B$ are the roots of $x^2-2x+2=0$ then ${\tan }^2(A+B)=$

• A. $4$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $4$

tan A and tan B are roots of the given quadratic equation.

$\Rightarrow \tan A+\tan B=2$ and $\tan A\times \tan B=2$

We expand the expression to be evaluated as

${\left(\tan (A+B)\right)}^2={\left(\frac{\tan A+\tan B}{1-\tan A\times \tan B}\right)}^2$

substituting the values we get

$={\left(\frac{2}{1-2}\right)}^2=4$