已知sin(α-π/4)=(7根号2)/10,cos2α=7/25,求sinα+cosα及tan(α+π/3)的值.

问题描述:

已知sin(α-π/4)=(7根号2)/10,cos2α=7/25,求sinα+cosα及tan(α+π/3)的值.

sin(α-π/4)=7√2/10=sinαcosπ/4-cosαsinπ/4=sinα√2/2-cosα√2/2 =√2/2(sinα-cosα)=7√2/10sinα-cosα=7/5cos2α=cos^2(α)-sin^2(α)=(sinα-cosα)(sinα+cosα)=7/257/5(sinα+cosα)=7/25sinα+...