Question

Find ℒ{f(t)} by first using a trigonometric identity. (write your answer as a function of s. ) f(t) = cos2(t)

Answer 1

The Laplace transform of f(t) = cos² t is equal to the following expression: $\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}$.

How to determine the Laplace transform of a non-simple trigonometric expression

In this we need to rewrite the given function in terms of sines and cosines, whose Laplace transforms are well known. There is the following trigonometric formula:

$\cos ^{2} t = \frac{1-\cos 2t}{2}$   (1)

Now we proceed to apply the Laplace transforms:

$\mathcal {L} \{f(t)\} = \frac{1}{2}\cdot \mathcal {L} \left\{1 \right\}-\frac{1}{2}\cdot \mathcal {L}\left\{\cos 2t\right\}$

$\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}$

The Laplace transform of f(t) = cos² t is equal to the following expression: $\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}$. $\blacksquare$

Remark

The statement is poorly formatted, the correct form is shown below:

Find $\mathcal {L}\{f(t)\}$ by first using a trigonometric expression. (Write your answer as a function of s). f(t) = cos² t

To learn more on Laplace transforms, we kindly invite to check this verified question: brainly.com/question/2088771