Question

find all solutions to the equation sin^2(2x)=1/4

Answer 1

you're going to be writing for a while.. (there's infinite solutions)

Answer 2

[0,2pi]

Answer 3

x = 1/12 (6 pi n+-pi)

Answer 4

\[\Large \sin^{2}(2x)=\frac{1}{4}\]
\[\Large \sin^{2}(2x)=\sin^{2}\frac{\pi}{6}\]

Now we know that for-
\[\Large \sin^{2}\theta=\sin^{2}\alpha\]
\[\Large \theta=n\pi \pm\alpha \]

substitute theta and alpha.