  In-plane torque measurements were performed on heavy fermion CeCoIn$_5$
single crystals in the temperature $T$ range 1.8 K $\leq T \leq 10$ K and
applied magnetic field $H$ up to 14 T. The normal-state torque is given by
$\tau_n \propto H^4(1+T/T_K)^{-1}\sin 4\phi$. The reversible part of the
mixed-state torque, obtained after subtracting the corresponding normal state
torque, shows also a four-fold symmetry. In addition, sharp peaks are present
in the irreversible torque at angles of $\pi/$4, 3$\pi$/4, 5$\pi$/4, 7$\pi$/4,
etc. Both the four-fold symmetry in the reversible torque and the sharp peaks
in the irreversible torque of the mixed state imply $d_{xy}$ symmetry of the
superconducting order parameter. The field and temperature dependences of the
reversible mixed-state torque provide further evidence for $d_{xy}$ wave
symmetry. The four-fold symmetry in the normal state has a different origin
since it has different field and temperature dependences than the one in the
mixed state. The possible reasons of the normal state four-fold symmetry are
discussed.
