UA-UMO 1999

Solve the equation $$(\sin x)^{1998}+(\cos x)^{-1999}=(\cos x)^{1998}+(\sin x)^{-1999}.$$

Let $AA_1,BB_1,CC_1$ be the altitudes of an acute-angled triangle $ABC$ , and let $O$ be an arbitrary interior point. Let $M,N,P,Q,R,S$ be the feet of the perpendiculars from $O$ to the lines $AA_1,BC,BB_1,CA,CC_1,AB$ , respectively. Prove that the lines $MN,PQ,RS$ are concurrent.