Question

Trigonometry question, can this be simplified?

Answer 1

\[\sqrt{(-e^{-t}\sin2t+e^{-t}2\cos2t)^2+(2e^{-t})^2+(-e^{-t}\cos2t-2e^{-t}\sin2t)^2}\]

Answer 2

If you were to multiply out the quantity under the radical sign, you'd find that every term has the factor \[e ^{-2t}\]

Answer 3

the square root of that is easily found. So, yes, you could begin simplification by expaning all powers under the radical and then factoring out \[e ^{-2t}\]

Answer 4

Once you've done that, other patterns may appear under the radical. Perhaps the radicand could be simplified further.