2. This problem will show you how to derive a formula for L{cos(bt)} without directly evaluating the integral by using the identity eta = cos(a) + i sin(a). a. Use the above identity to show that - elbt te-ibt 2 = cos(bt). b. Use the identity from part a and the linearity of the Laplace transform to evaluate L{cos(at)}. Make sure it agrees with what is shown in the table.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. This problem will show you how to derive a formula for £{cos(bt)} without directly
evaluating the integral by using the identity eia = cos(a) + i sin(a).
eibt +e-ibt
a.
Use the above identity to show that-
=
cos (bt).
2
b.
Use the identity from part a and the linearity of the Laplace transform to
evaluate L{cos(at)}. Make sure it agrees with what is shown in the table.
Transcribed Image Text:2. This problem will show you how to derive a formula for £{cos(bt)} without directly evaluating the integral by using the identity eia = cos(a) + i sin(a). eibt +e-ibt a. Use the above identity to show that- = cos (bt). 2 b. Use the identity from part a and the linearity of the Laplace transform to evaluate L{cos(at)}. Make sure it agrees with what is shown in the table.
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