Question

решите уравнегие

sinx-cosx=1​

Answer 1

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

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