  We develop an approach to study the entanglement in two coupled harmonic
oscillators. We start by introducing an unitary transformation to end up with
the solutions of the energy spectrum. These are used to construct the
corresponding coherent states through the standard way. To evaluate the degree
of the entanglement between the obtained states, we calculate the purity
function in terms of the coherent and number states, separately. The result is
yielded to two parameters dependance of the purity, which can be controlled
easily. Interesting results are derived by fixing the mixing angle of such
transformation as \pi/2. We compare our results with already published work and
point out the relevance of these findings to a systematic formulation of the
entanglement effect in two coupled harmonic oscillators.
