General solution for trigonometry equation How should I state the general solution for the equation $\sin(4\phi)=\cos(2\phi)$.
The angles are $15$, $45$, $75$ and $135$ if I restrict myself within the range $[0,360]$

As $\cos2\phi=\sin4\phi=\cos(90^\circ-4\phi)$
$\implies 2\phi=n360^\circ\pm(90^\circ-4\phi)$ where $n$ is any integer
Taking '+' sign, $2\phi=n360^\circ+90^\circ-4\phi$
$\implies 6\phi=n360^\circ+90^\circ \implies \phi=n60^\circ+15^\circ$
As $0\le \phi<360^\circ, 0\le n60^\circ+15^\circ<360^\circ\implies 0\le n\le 5$
Taking '-' sign, $2\phi=n360^\circ-90^\circ+4\phi$
$\implies 2\phi=90^\circ-n360^\circ\implies \phi=45^\circ-n180^\circ$
As $0\le \phi<360^\circ, 0\le 45^\circ-n180^\circ<360^\circ \implies -1\le n\le0$
So, there are $6+2=8$ solutions in $\in[0, 360^\circ)$
