`\sin^2 3x - \cos^2 4x = \sin^2 5x - \cos^2 6x`

`<=>\frac{1 - \cos6x}{2} - \frac{1 + \cos8x}{2} = \frac{1 - \cos10x}{2} - \frac{1 + \cos12x}{2}`

`<=>\frac{-\cos6x - \cos8x}{2} = \frac{-\cos10x - \cos12x}{2}`

`<=>-\cos6x - \cos8x = -\cos10x - \cos12x`

`<=>\cos10x + \cos12x - \cos6x - \cos8x = 0 `

`<=>2 \cos11x \cos x - 2 \cos7x \cos x = 0`

`<=>2 \cos x ( \cos11x - \cos7x) = 0`

TH1: `\cos x = 0 <=>x = \frac{\pi}{2} + k\pi, k \in ZZ`

TH2:`\cos11x = \cos7x`

`->11x = 7x + 2k\pi `hoặc `11x = -7x + 2k\pi`

`->x = \frac{k\pi}{2} `hoặc `x = \frac{k\pi}{9}`

`->S={ \frac{\pi}{2} + k\pi;  \frac{k\pi}{2}; \frac{k\pi}{9} |k\in ZZ} `