若cos2α/sin(α-π/4)则cosα+sinα的值为

若cos2a/sin((a-(π/4))=-(√2)/2，则cosa+sina的值为

解:由cos2α/sin(α-π/4)=-(√2)/2,

且
cos2α=cos²α-sin²α

sin(α-π/4)=(√2)/2*(sinα-cosα)

则:

cos2α/sin(α-π/4)=cos²α-sin²α/((√2)/2*(sinα-cosα))=-(√2)/2

等式左边同时约去sinα-cosα,可得:

√2(sinα+cosα)=-(√2)/2

则有:sinα+cosα=-1/2

cos2α/sin(α-π/4)=-根号2/2,则cosα+sinα的值为多少

cos2α=cos²α-sin²α
sin(α-π/4)=sinαcos(π/4)-sin(π/4)cosα

cos2α/sin(α-π/4)
=(cos²α-sin²α)/((根号2/2)sinα-(根号2/2)cosα)
=(cosα-sinα)(cosα+sinα)/[(根号2/2)(sinα-cosα)]
=-根号2(cosα+sinα)
=-根号2/2

所以cosα+sinα=1/2

条件不足