F (x) is continuous on [0, π] and differentiable in (0, π). It is proved that there is at least one point of ε in (0, π) such that f '(ε) sin ε + F (ε) cos ε = 0

F (x) is continuous on [0, π] and differentiable in (0, π). It is proved that there is at least one point of ε in (0, π) such that f '(ε) sin ε + F (ε) cos ε = 0


Let f (x) = f (x) SiNx, then f (x) is continuous on [0, π] and differentiable in (0, π), and f (0) = f (π) = 0. According to Rolle's theorem, there is a point ε∈ (0, π) such that f '(ε) = 0, that is, f' (ε) sin ε + F (ε) cos ε = 0

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