What is laplacetransform 3cos^2(t) ?

The answer to laplacetransform 3cos^2(t) is 3/(2s)+(3s)/(2(s^2+4))

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laplacetransform 3cos^2(t)

laplace transform

3 cos^{2} (t)

\frac{3}{2 s} + \frac{3 s}{2 ( s ^{2} + 4 )}

Solution steps

L {3 cos^{2} (t)}

Rewrite using trig identities

L {\frac{3}{2} + \frac{3}{2} cos (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 {\frac{3}{2}} + \frac{3}{2} L {cos (2 t)}

L {\frac{3}{2}} : \frac{3}{2 s}

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

= \frac{3}{2 s} + \frac{3}{2} \cdot \frac{s}{s ^{2} + 4}

Refine

\frac{3}{2 s} + \frac{3}{2} \frac{s}{s ^{2} + 4} : \frac{3}{2 s} + \frac{3 s}{2 ( s ^{2} + 4 )}

= \frac{3}{2 s} + \frac{3 s}{2 ( s ^{2} + 4 )}

What is laplacetransform 3cos^2(t) ?
The answer to laplacetransform 3cos^2(t) is 3/(2s)+(3s)/(2(s^2+4))