Question

Sa se calculeze tg($\frac{\pi }{2}$ - arctg$\frac{1}{2}$ ).

Ati putea sa imi spuneti si formula folosita pentru fiecare pas?

Answer 1

$\text{tg}\Big(\dfrac{\pi}{2} - \text{arctg}\Big(\dfrac{1}{2} \Big)\Big) = \text{ctg}}\Big(\text{arctg}\Big(\dfrac{1}{2} \Big)\Big) = \\ \\ \boxed{\text{Am folosit formula: } \text{tg}\Big(\frac{\pi}{2} -x\Big) = \text{ctg}(x)} \\ \\ = \dfrac{1}{\dfrac{1}{2}} = 2\\ \\ \boxed{\text{Am folosit formula: } \text{ctg}(\text{arctg}\,x) = \dfrac{1}{x}}$