What is laplacetransform sin(t)cos(t) ?

The answer to laplacetransform sin(t)cos(t) is 1/(s^2+4)

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laplacetransform sin(t)cos(t)

laplace transform

sin (t) cos (t)

\frac{1}{s ^{2} + 4}

Solution steps

L {sin (t) cos (t)}

Use the following identity:

cos (x) sin (x) = sin (2 x) \frac{1}{2}

= L {sin (2 t) \frac{1}{2}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{2} L {sin (2 t)}

L {sin (2 t)} : \frac{2}{s ^{2} + 4}

= \frac{1}{2} \cdot \frac{2}{s ^{2} + 4}

Refine

\frac{1}{2} \frac{2}{s ^{2} + 4} : \frac{1}{s ^{2} + 4}

= \frac{1}{s ^{2} + 4}

\frac{\partial}{\partial x} (5 x y e^{(x + y)})

\frac{d}{d x} (2 x + \frac{4 x}{3 x - 1})

f (x) = \frac{4 x}{x ^{2} - 5}, at x = 3

\int \frac{1}{x x ^{2} - 9} d x

\int_{0}^{2} 1

What is laplacetransform sin(t)cos(t) ?
The answer to laplacetransform sin(t)cos(t) is 1/(s^2+4)