已知(sinα+π/2)[1+tan(-α)]=1/2,则sinαcosα等于

问题描述:

已知(sinα+π/2)[1+tan(-α)]=1/2,则sinαcosα等于

(sinα+π/2)[1+tan(-α)]=1/2
cosα(1-tanα)=1/2
cosα(1-sinα/cosα)=1/2
cosα-sinα=1/2
cos^2α-2sinαcosα+sin^2α=1/4
1-1/4=2sinαcosα
sinαcosα=3/8