Have a question dealing with Laplace Transformations. Find the L{(1+cos2t)^2} I know the double angle theorem can translate this into cos^2(t) but we're missing a 1/2 from the equation. I know we can do a change of scale to get it to cos^2t but that does us no good.

Question

irishboy123 · Answer

expand to $1 +2 \cos 2 t+ \cos^2 2t$ 

then double angle formula $\cos 4t = 2 \cos^2 2t - 1$ so $\ \frac{1}{2} \cos 4t + \frac{1}{2} =  \cos^2 2t $ 

to get $2 \cos 2t+ \frac{1}{2}\cos 4t+\frac{3}{2}$ 

then $\mathcal{L}\{\cos (at) \}(p) =\frac{p^2}{p^2 + a^2}$

anonymous · Answer

Second problem you've solved for me irishboy thank you! This one really got me stumped.