Question 3
Let $x$ be the largest number in the interval $[0,2\pi]$ such that $(\sin x)^{2024}-(\cos x)^{2024}=1$. Find $\lfloor x\rfloor$.
(Note: If you think that such a number $x$ does not exist, enter your answer “99999”.)
(Note: If you think that such a number $x$ does not exist, enter your answer “99999”.)