Answer
See below
Work Step by Step
We are given: $f(t)=\cos t\\
g(t)=t$
Obtain: $(f * g)=\int^t_0f(t-x)g(x)dx\\
=\int^t_0 (t-x)\cos x dx\\
=\int^t_0[t\cos xdx-x\cos x]dx\\
=t\int^t_0 \cos x dx-\int^t_0 x\cos x dx\\
=\begin{vmatrix}
t\sin x-x\sin x-\cos x
\end{vmatrix}^t_0\\
=1-\cos t$
