Task 1. Solve the equation $\sqrt{2}|x+1| \sin x=x+1$.






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Answer. $-1 ; \frac{\pi}{4}+2 \pi n, n=0,1,2, \ldots ;-\frac{\pi}{4}+2 \pi n, n=-1,-2, \ldots ; \pm\left(\frac{3 \pi}{4}+2 \pi n\right), n=0,1,2, \ldots$