α是锐角,求证tanα﹢cotα﹢secα﹢cscα≥2(√2+1)

问题描述:

α是锐角,求证tanα﹢cotα﹢secα﹢cscα≥2(√2+1)

tana+cota+seca+csca
=1/(sinacosa)+(cosa+sina)/(sinacosa)
=(1+cosa+sina)/(sinacosa)
=(1+√2sin(a+45))/(sin2a/2)
=2(1+√2)/sin2a
0=2(√2+1)