Question

Решите уравнегие sinx-cosx=1​

Answer 1

$Sinx-Cosx=1\\\\\sqrt{1^{2}+1^{2}} =\sqrt{2}\\\\\sqrt{2}(\frac{1}{\sqrt{2}}Sinx-\frac{1}{\sqrt{2}} Cosx})=1\\\\\sqrt{2}(Sinx Cos\frac{\pi }{4}-Cosx Sin\frac{\pi }{4})=1\\\\\sqrt{2}Sin(x-\frac{\pi }{4})=1\\\\Sin(x-\frac{\pi }{4})=\frac{\sqrt{2} }{2}$

$1)x-\frac{\pi }{4}=\frac{\pi }{4}+2\pi n,n\in z\\\\x=\frac{\pi }{2}+2\pi n,n\in z\\\\2)x-\frac{\pi }{4}=\pi-\frac{\pi }{4}+2\pi n,n\in z\\\\x=\pi+2\pi n,n\in z$