In my textbook it says that to obatin the followin equation: $$ c_1 = \frac{F_0}{\sqrt{(k-m\Omega^2)^2+(\Omega r)^2}} $$
you have to put: $$ \tan \phi = - \frac{ \Omega r }{k-m \Omega^2} $$
into: $$ (-m\Omega^2 \cos \phi - r \Omega \sin \phi +k \cos \phi)c_1 = F_0 $$
yet I don't get it
If $\tan \phi = - \frac{ \Omega r }{k-m \Omega^2}$
then $\\ \sin\phi = -\frac {\Omega r}{\sqrt{(k-m \Omega^2)^2 + (\Omega r)^2}}\\ \cos\phi = \frac {(k-m \Omega^2)}{\sqrt{(k-m \Omega^2)^2 + (\Omega r)^2}}\\ $