Question

已知sin(∏-α)×cos(-8∏-α)=60/169,α∈（∏/4,∏/2),求sinα.cosα

Answer 1

sin(π-α)×cos(-8π-α)=60/169

sin(α)×cos(-α)=60/169

sinα×cosα=60/169

又∵sin²α+cos²α=(sinα+cosα)²-2sinα×cosα=1

∴(sinα+cosα)²=2sinα×cosα+1=289/169 ①

由sin²α+cos²α=(sinα-cosα)²+2sinα×cosα=1

得：(sinα-cosα)²=1-2sinα×cosα=49/169 ②

∵α∈（π/4,π/2),∴sinα+cosα>0,sinα-cosα