有两个函数f(x)=asin(kx+π／3),g(x)=btan(kx-π／3)(k>0),已知它们的周期和为3π／2,且f（π／2）＝g（π／2）,f（π／4）＝－√3g（π／4）＋1,求a、b、k的值

T1+T2=2π/|k|+2π/|2k|=3π/k=3π/2
k=2
f(x)=asin(2x-π/3)
g(x)=bcos(4x-π/6)
f(π/2)=asin(2π/3)=asin(π-π/3)=asin(π/3)=acos(π/2-π/6)=acos(π/6)=g(π/2)=bcos(-π/6)=bcos(π/6)
所以a=b
f(π/4)=asin(π/6)=-√3g(π/4)-1=-√3bcos(5π/6)-1
所以a/2=-√3*b(-√3/2)-1=3b/2-1
a=3b-2
a=b
所以a=b=1
f(x)=sin(2x-π/3)
g(x)=cos(4x-π/6)

F(x)周期为2π/k,G(x)周期为π/k,
3π/k=3π/2,k=2
F(x)=asin(2x+π／3),G(x)=btan(2x-π／3)
代入已知条件F（π／2）＝G（π／2）,F（π／4）＝－√3G（π／4）＋1,
再由诱导公式化简
得a=2b,a=-2b+2
a=1,b=1/2 ，k=2

f(x)=asin(kx+π／3),g(x)=btan(kx-π／3)(k>0),已知它们的周期和为2π/k+π/k=3π／2,∴k=2.又f（π／2）＝g（π／2）,f（π／4）＝－√3g（π／4）＋1,∴-a(√3）/2=-b√3,a/2=-√3*b（1-√3）/（1+√3）+1,化简得...