若x∈(0,90°),化简(根号1-sinx)/2
问题描述:
若x∈(0,90°),化简(根号1-sinx)/2
答
√[(1-sinx)/2]=√{[1-cos(90-x)]/2}=
√{[1-2cos(45-x/2)^2+1]/2}=√[1-cos(45-x/2)^2}=
√[sin(45+x/2)^2]=sin(45+x/2)
答
1-sinx=[sin(x/2)]^2+[cos(x/2)]^2-2sin(x/2)cos(x/2)=[sin(x/2)-cos(x/2)]^2