What is laplacetransform cos(2(t-(5pi)/4)) ?

The answer to laplacetransform cos(2(t-(5pi)/4)) is 2/(s^2+4)

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laplacetransform cos(2(t-(5pi)/4))

laplace transform

cos (2 (t - \frac{5 π}{4}))

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

Solution steps

L {cos (2 (t - \frac{5 π}{4}))}

Use Laplace Transform table:

L {cos (a t + b)} = \frac{s \cdot cos ( b ) - a \cdot sin ( b )}{s ^{2} + a ^{2}}

L {cos (2 (t - \frac{5 π}{4}))} = \frac{s cos ( - \frac{5 π}{2} ) - 2 sin ( - \frac{5 π}{2} )}{s ^{2} + 2 ^{2}}

= \frac{s cos ( - \frac{5 π}{2} ) - 2 sin ( - \frac{5 π}{2} )}{s ^{2} + 2 ^{2}}

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

What is laplacetransform cos(2(t-(5pi)/4)) ?
The answer to laplacetransform cos(2(t-(5pi)/4)) is 2/(s^2+4)