Question

1.已知角a的终边上有一点P(-根号3,m+1),m∈R,若cos a0,求实数m取值范围.

Answer 1

cos a = -√3/√[3+(m+1)]² 0 ==> m+1m sinAcosB + cosAsinB = 3/5

sin(A-B)=1/5 ==> sinAcosB - cosAsinB = 1/5

解得：

sinAcosB = 2/5

cosAsinB = 1/5

两式相除

==> (sinAcosB)/(cosAsinB) =2

==> tanA/tanB =2

即：tanA = 2tanB

(2) 设AB边上的高为h,则有：

h*cotA + h*cotB = AB = 3

==> h*(tanA+tanB)/(tanA*tanB) = 3

==> h * (tanA + 1/2*tanA)/(tanA*1/2*tanA) =3

==> h = tanA

由cosAsinB = 1/5 两边平方得：

cos²A(1-cos²B) =1/25；

将cos²A = 1/(1+tan²A)；cos²B = 1/(1+tan²B) = 1/(1+1/4*tan²A) 代入并整理得:

(tan²A -10)² = 96

解得：tan²A = 10±4√6

==> h = tanA = 2±√6

因此AB边上的高为2±√6