Question

(sinx+cosx)² -sin(2x)=1

Answer 1

$(\sin{x}+\cos{x})^2-\sin{2x}=1\\ \sin^2{x}+\cos^2{x}+2\sin{x}*\cos{x}-\sin{2x}=1\\ \sin^2{x}+\cos^2{x}+2\sin{x}*\cos{x}-(2\sin{x}*\cos{x})=1\\ 1+2\sin{x}*\cos{x}-(2\sin{x}*\cos{x})=1\\ 1=1$

Answer:$x \in (-\infty;\infty)$