要使等式sinA加cosA =(2m-3)/(2-m )有意义,求m的取值范围._数学解答

要使等式sinA加cosA =(2m-3)/(2-m )有意义,求m的取值范围.

人气：141 ℃　时间：2020-10-01 16:04:08

解答

sinA+cosA=(2m-3)/(2-m)
=√2sin(x+A)
值域为 [-√2,√2]
所以
|(2m-3)/(2-m)|≤√2
|[2(m-2)+1]/(m-2)|≤√2
|2+[1/(m-2)]|≤√2
-√2-2≤1/(m-2)≤√2-2
m-2