Simplifying $\cos(16t) \cos(6t)$ using Euler's formula

I have been tasked with simplifying this expression using Euler's equation:

$$f(t)=\cos(16t) \cos(6t)$$

I really can't figure out how to go about this. Can you push me in the right direction?

• I think this question is using an incorrect tag. 'eulers-constant' refers to $\gamma \approx 0.577$, not $e \approx 2.718$. – Bladewood Sep 17 '18 at 10:17

I think you are to derive one of the Werner Formulas using Intuition behind euler's formula

As $\cos y+i\sin y=e^{iy}, e^{-iy}=?$

$$e^{iy}+e^{-iy}=?, e^{iy}-e^{-iy}=?$$

Replace $\cos16t\cos6t$ with exponentials and then multiply out

replace back exponentials with cosines.

• I'm trying to make sense of what you've written and I almost get it I think.. but still not completely sure. With the Werner formula I can get: $2\,\cos \left( 16\,t \right) \cos \left( 6\,t \right) =\cos \left( 22 \,t \right) +\cos \left( 10\,t \right)$ Is that what you mean? – Boris Grunwald Sep 17 '18 at 10:26
• @Boris, Yes, u r right – lab bhattacharjee Sep 17 '18 at 11:09