Question

find laplace transform cos² wt​

Answer 1

Step-by-step explanation:

By indentity:

$\cos^{2}( { \alpha }) = \frac{1}{2} (1 + \cos(2 \alpha ) )$

Laplace transform is:

$l( { \cos ^{2} (wt) }) = \frac{1}{2} \times(l (1 \times \cos(2wt) )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times \: l(1 )\times l(1 + \cos(2wt) )$

$\: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times \frac{1}{s} \times \frac{s}{ {s}^{2} + {4w}^{2} }$