giải phương trình : sin^2 2x=1/2

Đáp án:

\(\left[ \begin{array}{l} x= \dfrac{\pi}{8}+k\pi\\x=\dfrac{3\pi}{8}+k\pi\\x= -\dfrac{\pi}{8}+k\pi\\x= \dfrac{5\pi}{8}+k\pi\end{array} \right.\)`(kinZZ)`

Giải thích các bước giải:

`sin^2 2x=1/2`

`<=>`\(\left[ \begin{array}{l}\sin 2x=\dfrac{\sqrt2}{2}\\\sin 2x=-\dfrac{\sqrt2}{2}\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}\sin 2x=\sin \dfrac{\pi}{4}\\\sin 2x=\sin \dfrac{-\pi}{4}\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l} 2x= \dfrac{\pi}{4}+k2\pi\\2x=\dfrac{3\pi}{4}+k2\pi\\2x= -\dfrac{\pi}{4}+k2\pi\\2x= \dfrac{5\pi}{4}+k2\pi\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l} x= \dfrac{\pi}{8}+k\pi\\x=\dfrac{3\pi}{8}+k\pi\\x= -\dfrac{\pi}{8}+k\pi\\x= \dfrac{5\pi}{8}+k\pi\end{array} \right.\)`(kinZZ)`