Question

$Calculati:\\ \\ arctg\frac{1}{2} +arctg\frac{1}{3} .$

Answer 1

$\text{Folosesti formula:}\\\boxed{arctg\ a+arctg\ b=arctg \left(\dfrac{ a+ b}{1- a\cdot b}\right)} arctg\ \dfrac{1}{2}+arctg\ \dfrac{1}{3}=arctg\left(\dfrac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\cdot \frac{1}{3}}\right)=arctg\ \dfrac{\frac{5}{6}}{1-\frac{1}{6}}\right)=arctg\ 1=\dfrac{\pi}{4}$