If $ an A=\frac{5}{6}, an B=\frac{1}{11}$, then $A+B=$

Question

If $	an A=\frac{5}{6}, 	an B=\frac{1}{11}$, then $A+B=$

Aicharya · Accepted Answer

$\begin{aligned} 	an (A+B) &=\frac{	an A+	an B}{1-	an A 	an B} \ &=\frac{\frac{5}{6}+\frac{1}{11}}{1-\frac{5}{6} 	imes \frac{1}{11}}=\frac{\frac{55+6}{66}}{1-\frac{5}{66}}=\frac{\left(\frac{61}{66}ight)}{\left(\frac{61}{66}ight)} \ 	an (A+B) &=1 \Rightarrow A+B=	an ^{-1}(1) \Rightarrow A+B=\frac{\pi}{4} \end{aligned}$

If $\tan A=\frac{5}{6}, \tan B=\frac{1}{11}$, then $A+B=$

Solution