已知sin(a-π/4)=7√2/10,cos2a=7/25求sina及tan(a+π/3)

题目

已知sin(a-π/4)=7√2/10,cos2a=7/25求sina及tan(a+π/3)

答案

∵sin(a-π/4)=7√2/10∴√2/2sina-√2/2cosa=7√2/10∴sina-cosa=7/5 ①∵,cos2a=7/25∴cos2a=cos²a-sin²a=(cosa-sina)(cosa+sina)∴(cosa-sina)(cosa+sina)=7/25∴-7/5(cosa+sina)=7/25∴sina+cosa=-1/5...