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Prove that: (cos4x+cos3x+cos2x)/(sin4x+s...

Prove that: `(cos4x+cos3x+cos2x)/(sin4x+sin3x+sin2x)=cot3x`

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`frac{cos 4 x+cos 3 x+cos 2 x}{sin 4 x+sin 3 x+sin 2 x}`

`=frac{(cos 4 x+cos 2 x)+cos 3 x}{(sin 4 x+sin 2 x)+sin 3 x}`

`=frac{2 cos 3 x cos x+cos 3 x}{2 sin 3 x cos x+sin 3 x}`

`=frac{cos 3 x[2 cos x+1]}{sin 3 x[2 cos x+1]}`

`=cot 3 x`

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