Solution:
According to the question, two points P and Q make an angle α at the origin. This is shown in the figure:
It can be observed from the figure that points P, O and Q form a triangle. So, in ΔOPQ by using cosine formula we have:
\[\cos \alpha =\frac{O{{P}^{2}}+O{{Q}^{2}}-P{{Q}^{2}}}{2OP.OQ}\]