Question

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

• A. $\frac{4}{5}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{1}{4}$

Answer 1

Answer: (D)

$\frac{1}{4}$

$x^2-2x+2=0$

$\tan A+\tan B=\frac{-(-2)}{1}=2$

$\tan A.\tan B=\frac{2}{1}=2$

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}=\frac{2}{1-2}=-2$

${\tan }^2(A+B)=4$

${\cot }^2(A+B)=\frac{1}{4}$