Question

已知-π/2<α<0,且函数f(α)=cos(3π/2+α)-sinα*√(1+cosα)/(1- cosα) -1(ps:-1在根号外面)

1.化简f(α)
2.若f(α)=1/5,求sinα*cosα和sinα-cosα的值.
越快越好 要详细步骤!

Answer 1

f(α)=cos(3π/2+α)-sinα*√(1+cosα)/(1- cosα) -1=sinα-sinα√镇友铅告盯(1+cosα)^2/sin^2α-1
=sinα-sinα|1+cosα|/|sinα|-1=sinα+1+cosα-1==sinα+cosα

f(α)=1/5=sinα+cosα, 1+2sinαcosα=1/25, sinαcosα=-12/25,
(sinα-cosα)^2=1-2sinαcosα=49/25, sinα-cosα=7/御好5