I have the below equation:
$$ F(t)=(k_1 e^{at} + (k_{Re}-ik_{Im})(\lambda+i\omega)e^{(\lambda+i\omega)t}+(k_{Re}+ik_{Im})(\lambda-i\omega)e^{(\lambda-i\omega)t})/((r_1k_1 e^{at} + r_2(k_{Re}-ik_{Im})(\lambda+i\omega)e^{(\lambda+i\omega)t}+r_3(k_{Re}+ik_{Im})(\lambda-i\omega)e^{(\lambda-i\omega)t})) $$
where $r_1, r_2$ and $r_3$ also have real and Imaginary parts. Plotting the equation, it has below form:
$$ F(t) = C_1 - C_2 cot( \omega t ) $$
My question is: Is it possible to achieve to $cot( \omega t)$ form analytically? and how!
Thank you in advanced!