Question

√(2)*sinX-√(2)*cosX=1

Answer 1

$mathtt{sqrt{2}sinx-sqrt{2}cosx=1;~sinx-cosx=frac{1}{sqrt{2}};~}\\mathtt{sqrt{2}sin(x-frac{pi}{4})=frac{sqrt{2}}{2};~sin(x-frac{pi}{4})=frac{1}{2};~left[begin{array}{ccc}mathtt{x-frac{pi}{4}=frac{pi}{6}+2npi}\mathtt{x-frac{pi}{4}=frac{2pi}{3}+2npi}end{array}right}$

ОТВЕТ: $mathtt{left[begin{array}{ccc}mathtt{x=frac{5pi}{12}+2npi}\\mathtt{x=frac{11pi}{12}+2npi}end{array}right,~nin Z}$