若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?知道的请写步骤~其中a为角度

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若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?知道的请写步骤~其中a为角度
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若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?知道的请写步骤~其中a为角度
若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?
知道的请写步骤~其中a为角度

若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?知道的请写步骤~其中a为角度
cos2a/sin(a-π/4)=(2cos2a*cos(a-π/4)) /(2sin(a-π/4) cos(a-π/4))
cos2a/sin(a-π/4)=(2cos2a*cos(a-π/4)) /sin(2a-π/2)
cos2a/sin(a-π/4)=-(2cos2a*cos(a-π/4)) /cos2a
cos2a/sin(a-π/4)=-2*cos(a-π/4)
-2*cos(a-π/4) =-√2/2
cos(a-π/4) =√2/4
cosa*cos(π/4)+sina*sin(π/4)=√2/4
cosa+cosb=1/2

cos2a/sin(a-π/4)
=(cos²a-sin²a)/[(√2/2)(sina-cosa)]
=(cosa+sina)(cosa-sina)/[(√2/2)(sina-cosa)]
=-(cosa+sina)/(√2/2)
=-√2/2
所以
cosa+sina=1/2

cos2a/sin(a-π/4)=-√2/2
√2(cosa-sina)(cosa+sina)/(sina-cosa)=-√2/2
cosa+sina=1/2