三角函数式的化简与证明（二）

一、化简√[1/(cosα)^2 - 1 ] =√[1/(cosα)^2 - (cosα)^2/(cosα)^2 ]=√{ [ 1 - (cosα)^2 ]/(cosα)^2 } =√{ [ (sinα)^2 ]/(cosα)^2 }=sinα/cosα = tanα 。三、证明左边 (cosα)^2 *(tanα)^2 +(cosα)^2=(cosα)^2 *(sinα)^2/(cosα)^2 +(cosα)^2=(sinα)^2 +(cosα)^2= 1 =右边。证毕。