Is the Laplace Transform Calculation Correct for a Given Function?

[ineedhelpnow]

Did I do this right?View image: 20151201 152557

 

[Prove It]

Did I do this right?View image: 20151201 152557

Why did you out of the blue change sin(5t) to cos(5t)?

 

[ineedhelpnow]

i made an oopsie :) thanks for pointing that out. is the rest of it correct though? because i did the rest of the work with sin. not cos