Question

Angles $A$ and $B$ are obtuse angles such that, $\tan A+\tan B+\tan A\tan B=1$. If $A-B={41}^{\circ }$ then

• A. $A={133}^{\circ },B={92}^{\circ }$
• B. $A={143}^{\circ },B={102}^{\circ }$
• C. $A={173}^{\circ },B={132}^{\circ }$
• D. $A={163}^{\circ },B={122}^{\circ }$

Answer 1

Answer: (A)

$A={133}^{\circ },B={92}^{\circ }$

$\tan A+\tan B+\tan A\tan B=1$
$\tan A+\tan B=1-\tan A\tan B$
$\frac{\tan A+\tan B}{1-\tan AtanB}=1$
$\tan (A+B)=\tan 225$ (Since, both $A$ and $B$ are obtuse)
$A+B=225$
Also, $A-B=41$
Adding the two equations,
$2A=266$
$A={133}^{\circ }$
and, $B=133-41={92}^{\circ }$