Đáp án: $x=\dfrac{π}{2}+kπ;x=k \dfrac{π}{5};x=k\dfrac{π}{2}$ `(k \in ZZ)`
Giải thích các bước giải:
` sin^2 x+ sin^2 2x = sin^2 3x +sin^2 4x`
`<=> (1-cos2x)/2 + (1-cos4x)/2 = (1-cos6x)/2 + (1-cos8x)/2`
`<=> cos2x+cos4x=cosx6x+cos8x`
`<=> 2cos3xcosx = 2cos7xcosx`
`<=> cosx(cos3x-cos7x)=0`
`<=> cosx.sin5x.sin2x=0`
`<=>` \(\left[ \begin{array}{l}x=\dfrac{π}{2}+kπ\\x=k \dfrac{π}{5}\\x=k\dfrac{π}{2}\end{array} \right.\) `(k \in ZZ)`
