What is laplacetransform sin(4t)cos(4t) ?

The answer to laplacetransform sin(4t)cos(4t) is 4/(s^2+64)

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laplacetransform sin(4t)cos(4t)

laplace transform

sin (4 t) cos (4 t)

\frac{4}{s ^{2} + 64}

Solution steps

L {sin (4 t) cos (4 t)}

Rewrite using trig identities

L {\frac{1}{2} sin (8 t)}

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 (8 t)}

L {sin (8 t)} : \frac{8}{s ^{2} + 64}

= \frac{1}{2} \cdot \frac{8}{s ^{2} + 64}

Refine

\frac{1}{2} \frac{8}{s ^{2} + 64} : \frac{4}{s ^{2} + 64}

= \frac{4}{s ^{2} + 64}

\frac{d}{d x} ((3 x^{2} + 5 x) e^{x})

f (x) = 2 x - 2 x

\int sec^{5} (5 x) d x

\frac{\partial}{\partial x} (7 x y e^{- x^{2} - y^{2}})

\int \frac{1}{49 e ^{- 3 x} + e ^{3 x}} d x

What is laplacetransform sin(4t)cos(4t) ?
The answer to laplacetransform sin(4t)cos(4t) is 4/(s^2+64)