Fourier Transform of Cosine Function with Step Function Constraints

[electron2]

$$f(t-a)u_a(t)->F(s)e^{-as}$$
$$g(t)={\cos (t),0<=t<\pi}$$
$$g(t)={0,t>=\pi}$$

$$g(t)=\cos(t)[ u(t)-u(t-\pi)]=\cos(t) u(t)-\cos(t) u(t-\pi)=\frac{s}{s^2-1}+??\\$$

i can't apply the formula in the last part

 

[HallsofIvy]

Trig formula $cos(t-\pi)= -cos(t)$.

 

[electron2]

$$g(t)=\cos(t)[ u(t)-u(t-\pi)]=\cos(t) u(t)+\cos(t-\pi) u(t-\pi)=\frac{s}{s^2-1}+\frac{s}{s^2-1}e^{-\pi}\\$$

is it correct?