What is laplacetransform (sin(t)+cos(t))^2 ?

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

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laplacetransform (sin(t)+cos(t))^2

laplace transform

(sin (t) + cos (t))^{2}

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

Solution steps

L {(sin (t) + cos (t))^{2}}

Expand

(sin (t) + cos (t))^{2} : sin^{2} (t) + 2 sin (t) cos (t) + cos^{2} (t)

= L {sin^{2} (t) + 2 sin (t) cos (t) + cos^{2} (t)}

Rewrite using trig identities

L {1 + sin (2 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {1} + L {sin (2 t)}

L {1} : \frac{1}{s}

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

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

(0.91) \cdot (2.3)^{- 0.157}

e^{- 1.09861}

35 x^{2} y^{3} y

e^{- 3 x} e^{2 x}

\frac{( e ^{x} )}{e ^{x}}

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