If $ an A=\frac{1}{2}, an B=\frac{1}{3}$ then $ an (A+2 B)$ has the value

Question

If $	an A=\frac{1}{2}, 	an B=\frac{1}{3}$ then $	an (A+2 B)$ has the value

Aicharya · Accepted Answer

$	an A=\frac{1}{2}, 	an B=\frac{1}{3}$ [given] we have $	an 2 B=\frac{2 	an B}{1-	an ^2 B}=\frac{3}{4}$ $\because 	an (A+2 B)=\frac{	an A+	an 2 B}{1-	an A \cdot 	an 2 B}=\frac{\frac{1}{2}+\frac{3}{4}}{1-\frac{1}{2} 	imes \frac{3}{4}}=\frac{\frac{5}{4}}{\frac{5}{8}}=2$

If $\tan A=\frac{1}{2}, \tan B=\frac{1}{3}$ then $\tan (A+2 B)$ has the value

Solution