That's not true. Hypothetical existence of tachyons in no way affects the invariance of light speed.Actually, it's impossible to show. I suspect what you mean is that you can use the equations of special relativity to show it. But those equations are built on a foundation that contradicts your premise!
The foundation of special relativity is that light speed is invariant. You start out stating "if you do faster-than-light". That violates the foundation that light speed is invariant. Therefore whatever conclusions you draw are bound to be incorrect.