Question

how to simplify sqrt(e^(2t)+e^(-2t)+2)?

Answer 1

hint: comlete the square to get sqrt(e^t+e^-t)^2)=e^t+e^-t

Answer 2

Hint:\[\large\begin{align*}e^{2t}+e^{-2t}+2&=e^{-2t}\left(e^{4t}+2e^{2t}+1\right)\\\\
&=\left(e^{-t}\right)^2\left(e^{2t}+1\right)^2\\\\
&=\left(e^{-t}\left(e^{2t}+1\right)\right)^2\\\\
&=\left(e^{t}+e^{-t}\right)^2\end{align*}\]