Question

What is the difference between the graph of `f(x)=sin(4x)` and that of `f(x)=sin(5x)cosx-cos(5x)sinx`?

Answer 1

They are same.

Explanation:

Graph of `f(x)=sin(4x)` is as follows:
graph{sin(4x) [-5, 5, -2.46, 2.54]}

Graph of `g(x)=sin(5x)cosx-cos(5x)sinx` is as follows:
graph{sin(5x)cosx-cos(5x)sinx [-5, 5, -2.46, 2.54]}

It is evident that the two are identical. The reason is that `sin(4x)=sin(5x)cosx-cos(5x)sinx`

This is as `sin(A-B)=sinAcosB-cosBsinA` and putting `A=5x` and `B=x` we get above result.