F.4 A.maths歸約公式 help me!!!!!!

By using formula:
cos(A-B)=cosAcosB+sinAsinB
Sub A=nx and B=x, we have:
cos(nx-x)=cosnxcosx+sinnxsinx
cos(n-1)x=cosnxcosx+sinnxsinx
sinnxsinx=cos(n-1)x-cosnxcosx

formula: cos(A-B)=cosAcosB+sinAsinB
Let nx=A, x=B

cos(nx-x) = cosnx cosx- sinnx sinx
cos(n-1)x = cosx cos(nx)- sin(nx)sinx
sin(nx)sinx= cos(n-1)x-cosx cos(nx)