Question

a+b ??? Помогите с решением!!! Ответ 5п/4 (C)​

Answer 1

$tg(\alpha +\beta )=\frac{tg\alpha+tg\beta}{1-tg\alpha*tg\beta}=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}*\frac{1}{3}}=\frac{\frac{5}{6}}{1-\frac{1}{6}}=\frac{5}{6}:\frac{5}{6}=1\\\\tg(\alpha+\beta)=1\\\\\alpha+\beta=arctg1+\pi n,n\in Z\\\\\alpha +\beta=\frac{\pi }{4}+\pi n,n\in Z\\\\\pi<\alpha+\beta<2\pi\\\\\pi<\frac{\pi }{4}+\pi n<2\pi|:\pi\\\\1<\frac{1}{4}+n<2\\\\1-\frac{1}{4}<\frac{1}{4}-\frac{1}{4}+n<2-\frac{1}{4}$

$\frac{3}{4}<n<\frac{7}{4}\\\\n\in Z \Rightarrow n=1\\\\\alpha+\beta=\frac{\pi }{4}+\pi *1=\frac{\pi }{4}+\pi=\frac{5\pi }{4}\\\\Otvet:\boxed{\alpha+\beta =\frac{5\pi }{4}}$