What is laplacetransform cos(t+pi/4) ?

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

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laplacetransform cos(t+pi/4)

laplace transform

cos (t + \frac{π}{4})

\frac{s - 1}{2 ( s ^{2} + 1 )}

Solution steps

L {cos (t + \frac{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 (t + \frac{π}{4})} = \frac{s cos ( \frac{π}{4} ) - 1 \cdot sin ( \frac{π}{4} )}{s ^{2} + 1 ^{2}}

= \frac{s cos ( \frac{π}{4} ) - 1 \cdot sin ( \frac{π}{4} )}{s ^{2} + 1 ^{2}}

= \frac{s - 1}{2 ( s ^{2} + 1 )}

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