Đáp án:
``\(\left[ \begin{array}{l}x=\frac{\pi}{8}+\frac{k\pi}{4}\\x=±\frac{\pi}{3}+k\pi\end{array} \right.\) `(k∈ZZ)`
Giải thích các bước giải:
`sin^2x+sin^2 2x+sin^2 3x=3/2`
`⇔\frac{1-cos2x}{2}+\frac{1-cos4x}{2}+\frac{1-cos6x}{2}=3/2`
`⇔3-cos2x-cos4x-cos6x=3`
`<=>cos2x+cos4x+cos6x=0`
`<=>(cos2x+cos6x)+cos4x=0`
`<=>2cos4xcos2x+cos4x=0`
`<=>cos4x(2cos2x+1)=0`
`<=>`\(\left[ \begin{array}{l}\cos4x=0\\\cos2x=-\frac{1}{2}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}4x=\frac{\pi}{2}+k\pi\\2x=±\frac{2\pi}{3}+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\frac{\pi}{8}+\frac{k\pi}{4}\\x=±\frac{\pi}{3}+k\pi\end{array} \right.\) `(k∈ZZ)`
