= Solution
The <cosine function> is positive on $(0,\pi/2)$ and negative on $(\pi/2,2)$. Thus any nonzero $\alpha$ makes $\alpha\cos x$ negative on an interval of positive length. Taking $\alpha=0$ makes the total <definite integral> zero. Hence
$$
\boxed{\text{No real value of }\alpha\text{ gives a probability density.}}
$$
Normalization alone would suggest $\alpha=1/\sin2$, but that candidate still violates nonnegativity and therefore is not a <probability density function>.
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