α β 为锐角sin^4α/cos^2β+cos^4α/sin^2β=1,证α+ β=π/2

问题描述:

α β 为锐角sin^4α/cos^2β+cos^4α/sin^2β=1,证α+ β=π/2

∵(sinα)^4/(cosβ)^2+(cosα)^4/(sinβ)^2=1,∴(sinα)^4(sinβ)^2+(cosα)^4(cosβ)^2=(sinβ)^2(cosβ)^2,∴[1-(cosα)^2]^2(sinβ)^2+(cosα)^4(cosβ)^2=(sinβ)^2(c...