Difficulty with a Fourier Transform
It is easy to see that using the trigonometric identity in Equation $(1)$ below
$$
\cos(\theta_1 \pm \theta_2) = \cos(\theta_1)\cos(\theta_2) \mp \sin(\theta_1)\sin(\theta_2) \tag{1}
$$
We have
\begin{align}
f(t)\cos\big(\pi(t - 1)\big) &amp;= f(t)\overbrace{\cos(\pi t - \pi)}^{\text{use Equation}\ (1)}\\
&amp;\equiv -f(t)\cos(\pi t)\tag{2}
\end{align}
Which can be rewritten as
$$
-f(t)\cos(\pi t) = -f(t)\cos\left(2\pi \frac t2\right) = -f(t)\cos(2\pi f_c t)\quad\text{where}\quad f_c = \frac 12 
$$
And we know the Fourier cosine modulation frequency-shift property in equation $(3)$:
$$
\mathcal F\big\{x(t)\cos(2\pi f_c t)\big\} = \frac 12\big[X\left(f - f_c\right) + X\left(f + f_c\right)\big]\tag{3}
$$
You can now easily use Equation $(2)$ and $(3)$ to find the solution.