Question

дано..... найдите значение к... пожалуйста!!​

Answer 1

Ответ:

$arcsin(sin\dfrac{\pi}{3})+2arctg\dfrac{\sqrt3}{3}-arccos(-\dfrac{1}{2})+arcctg(-1)=k\pi \ ;\\\\\\arcsin(sin\dfrac{\pi}{3})+2arctg\dfrac{\sqrt3}{3}-arccos(-\dfrac{1}{2})+arcctg(-1)=\\\\\\=\dfrac{\pi}{3}+2\cdot \dfrac{\pi}{6}-(\pi -arccos\dfrac{1}{2})+(\pi -arcctg1)=\\\\\\=\dfrac{\pi}{3}+\dfrac{\pi}{3}-\pi +\dfrac{\pi}{3}+\pi -\dfrac{\pi}{4}=3\cdot \dfrac{\pi }{3}-\dfrac{\pi}{4}=\pi -\dfrac{\pi }{4}=\dfrac{3\pi }{4}\\\\\\\dfrac{3\pi }{4}=k\pi \ \ \ \ \Rightarrow \ \ \ k=\dfrac{3}{4}$