1.若cos2a/sin(a-π/4)=-2根号2,则cosa+sina的值为?2.在区间【-1,1】上随机取一个数x,

1 cos2a/sin(a-π/4)=sin2(π/4-a)/sin(a-π/4)=2sin(π/4-a)cos(π/4-a)/sin(a-π/4)=-2cos(π/4-a)=-2根号2
所以cos(π/4-a)=根号2
所以cosa+sina=cos(π/4-a)=根号2
2 令cos(πx/2)=0,得x=所有奇数
令cos(πx/2)=1/2,得x=2/3+4k或10/3+4k
因为x∈【-1,1】,做出cos(πx/2)的图像,可得cos(πx/2)的值介于0到1/2之间的区间是【-1,-2/3】或【2/3,1】
所以cos(πx/2)的值介于0到1/2之间的概率为（1/3+1/3）/2=1/3

cos2a/sin(a-π/4)=(2cos2a*cos(a-π/4)) /(2sin(a-π/4) cos(a-π/4))
1 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(...

【1】=2 化解 cos2a/sin(a-π/4）=【（cosa-sina）（cosa+sina）】/【（根号2）/2（sina-cosa）】
即-（cosa+sina）/（根号2）/2=)=-2根号2 cosa+sina=2