已知cos2α/sin(α-π/4)=-√2/5(1)求cosα+sinα的值;(2)若-π
问题描述：
已知cos2α/sin(α-π/4)=-√2/5
(1)求cosα+sinα的值;
(2)若-π
答
cos2α/sin(α-π/4)=-√2/5
cos2α=-√2/5sin(α-π/4)
(cos²α-sin²α)=-√2/5[sinαcos(π/4)-cosαsin(π/4)]=(cosα-sinα)/5
(cosα+sinα)(cosα-sinα)=(cosα-sinα)/5
所以 cosα+sinα=1/5 (1)
平方
1+2sinαcosα=1/25
2sinαcosα=-24/25 -π(cosα-sinα)²=1-2sinαcosα=49/25
因为 -π/2cosα-sinα>0
cosα-sinα=7/5
sinα-cosα=-7/5
答
sα的
答
cos2α/sin(α-π/4)=-√2/5(cos²a-sin²a)/[(√2/2)(sina-cosa)]=-√2/5-(cosa-sina)(cosa+sina)/[(√2/2)(cosa-sina)]=-√2/5-√2(cosa+sina)=-√2/5得 cosa+sina=1/5sinα-cosα=√2sin(a-π/4)-π...