1
(sinA-cosA)^2=1-2sinAcosA=1/4
sinAcosA=3/8
tanA+cotA=sinA/cosA+cosA/sinA=1/sinAcosA=8/3
2
-1≤m-2≤1
1≤m≤3
3
√3(tan40°-tan10°)-tan40°tan10°
=√3tan30°(1+tan40°tan10°)-tan40°tan10°
=1
4
tanA+tanB=-3
tanAtanB=-2
cot(A+B)=1/tan(A+B)=(1-tanAtanB)/(tanA+tanB)=(1+2)/-3=-1
5
由已知得
A点距离塔底的距离等于塔高
设塔高为xm
tan60°=x/(x-100)=√3
x=150+50√3
6
-1≤sinx≤1,-1≤cos2x≤1
-6≤6sinx≤6,
-9≤6sinx+cosx-2≤5
即：-9≤f(x)≤5
7
cos(2A+B)/sina+2sin(A+B)
=cos[A+(A+B)]/sinA+2sinAsin(A+B)/sinA
=[cosAcos(A+B)-sinAsin(A+B)+2sinAsin(A+B)]/sinA
=[cosAcos(A+B)+sinAsin(A+B)]/sinA
=cos[(A+B)-A]/sinA
=cosB/sinA
8
cosC=4/5,则,sinC=3/5
S=1/2absinC=1/2*3/5*ab=6
ab=20
a=20/b
a+b=9
b=4或b=5
a=5或a=4