F(x)=[(sinx)^2+1/(2010sinx)]*[(cosx)^2+1/(2010cosx)]≥ 2sinx/[√2010sinx)]*2cosx/[√(2010cosx)]=4/2010 /√[sinxcosx]=2/1005 /√[1/2*sin2x] ∵ 0≥2/1005 /√[1/2]≥2√2 /1005
