 Solution

On the specified domain $\sin x\ne 0$, so multiplying by $\sin x$ is legitimate. Use the double-angle identity to findThe first factor gives $x=\pm \pi /2$. The second gives ${\sin }^{2}x=1/2$, yielding four more values in the interval. ThusEvery listed value has nonzero sine and satisfies the original equation. Dividing by $\cos x$ would incorrectly lose the two solutions $\pm \pi /2$.