`ĐK: x \ne \pi/2+k\pi;x \ne \pi/10+k\pi/5;x \ne \pi/18+k\pi/9`
`tan x+tan 5x+tan 9x=tan x .tan 5x.tan 9x`
`<=>[sin x]/[cos x]+[sin 5x]/[cos 5x]+[sin 9x]/[cos 9x]=[sin x.sin 5x.sin 9x]/[cos x.cos 5x.cos 9x]`
`<=>sin x.cos 5x.cos 9x+sin 5x.cos x.cos 9x+sin 9x.cos x.cos 5x=sin x.sin 5x.sin 9x`
`<=>1/2(-sin 4x+sin 6x).cos 9x+1/2(sin 4x+sin 6x)cos 9x+1/2(sin 8x+sin 10x).cos 5x=1/2(cos 4x-cos 6x).sin 9x`
`<=>-1/2sin 4x.cos 9x+1/2sin 6x.cos 9x+1/2sin 4x.cos 9x+1/2sin 6x.cos 9x+1/2sin 8x.cos 5x+1/2sin 10x.cos 5x=1/2cos 4x.sin 9x-1/2cos 6x.sin 9x`
`<=>1/2cos 4x.sin 9x-3/2cos 6x.sin 9x=1/2sin 8x.cos 5x+1/2sin 10x.cos 5x`
`<=>sin 9x.cos 4x-3sin 9x.cos 6x=sin 8x.cos 5x+sin 10.cos 5x`
`<=>1/2(sin 5x+sin 13x)-3/2(sin 3x+sin 15x)=1/2(sin 3x+sin 13x)+1/2(sin 5x+sin 15x)`
`<=>1/2sin 5x+1/2sin 13x-3/2sin 3x-3/2sin 15x=1/2sin 3x+1/2sin 13x+1/2sin 5x+1/2sin 15x`
`<=>-2sin 3x=2sin 15x`
`<=>sin 15x=-sin 3x`
`<=>sin 15x=sin(-3x)`
`<=>[(15x=-3x+k2\pi),(15x=\pi+3x+k2\pi):}`
`<=>[(x=k\pi/9),(x=\pi/12+k\pi/6):}` `(k in ZZ)` (t/m)
