將tanx、cotx、secx、cscx全部用sinx和cosx代替,得：
y = six+cosx +(1+sinx+cosx)/(sinxcosx)
記 t = sinx+cosx ,則
2sinxcosx = (sinx+cosx)²-1 = t²-1
sinxcosx = (t²-1)/2
于是,
y = t + 2(1+t)/(t²-1) = t + 2/(t-1)
= (t-1) + 2/(t-1) + 1
直接用均值不等式,有
∴|y|≥2√2+1