Find the values of $x$ such that the following inequality holds: $\min\{\sin x,\cos x\}<\min\{1-\sin x,1-\cos x\}$
Problem
Source: Ukrainian National Math Olympiad 4th round
Tags: inequalities, trigonometry, algebra unsolved, algebra
Source: Ukrainian National Math Olympiad 4th round
Tags: inequalities, trigonometry, algebra unsolved, algebra
Find the values of $x$ such that the following inequality holds: $\min\{\sin x,\cos x\}<\min\{1-\sin x,1-\cos x\}$