TITLE: $\sin(4\theta) = \sin(2\theta+\pi/2)$ solve for $\theta$ when $\theta \in [0,\pi/4]$
QUESTION [0 upvotes]: According to Wolfram, doing the inverse on both sides gives $4\theta = 2\theta + \pi/2 + 2\pi n_1$, makes sense, but it also gives $4\theta = -2\theta + \pi/2+2\pi n_2$. This is what i don't understand, why do you also get a minus?

REPLY [0 votes]: Hint: your equation is equivalent to $\cos 2\theta (2\sin 2\theta -1)=0$. Note that $\arcsin\frac12=\frac{\pi}{6}$.

REPLY [0 votes]: If $\sin x = \sin y$, then either $x=y+2\pi n_1$, or $x=\pi-y+2\pi n_2$.
Now put $x=4\theta$ and $y=2\theta+\pi/2$.
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