已知:cos2a 除以 sin(a-pai/4) = 负的2分支根号2 求:cosa + sina =多少?

问题描述:

已知:cos2a 除以 sin(a-pai/4) = 负的2分支根号2 求:cosa + sina =多少?
A:负的2分支根号7 B:-1/2
C:1/2 D:2分支根号7

cos2a=cosa^2-sina^2=(cosa+sina)*(cosa-sina)
sin(a-π/4)=sina*cos(π/4)-cosa*sin(π/4)=√2(sina-cosa)/2
cos2a 除以 sin(a-pai/4) = 负的2分支根号2
即:(cosa+sina)*(cosa-sina)/[√2(sina-cosa)/2]=-√2/2
故cosa+sina=1/2
选C