Question

laplace sin2t*sin3t
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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)

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