Question

Laplace transform of sin2tsin3t​

Answer 1

Answer:

The product of sins can be converted into sum of cosines using the following formula-

(sinc) *(sind) = [cos(c-d) - cos(c+d)]/2

[You can verify it by expanding as cos(c+d) = cosc*cosd - sinc*sind]

Putting c=3t and d=2t, we have

sin3t.sin2t = [cost-cos5t]/2

So, Laplace transform by applying the linearity property will be -

[s/(s2+1)−s/( s2+25) ]/2

As Laplace transform of cos(at)= s/(s2 +a2)

I hope this is helpful to you.

If you have any query, feel free to ask in the comments section.

And if not, don't forget to upvote!