L.H.S: (√3 + 1) (3 – cot 30°)

= (√3 + 1) (3 – √3) [∵cos 30° = √3]

= (√3 + 1) √3 (√3 - 1) [∵(3 – √3) = √3 (√3 - 1)]

= ((√3)²– 1) √3 [∵ (√3+1)(√3-1) = ((√3)² – 1)]

= (3-1) √3

= 2√3

Similarly solving R.H.S: tan³ 60° - 2 sin 60°

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= 3√3 - √3

= 2√3

∴ L.H.S = R.H.S

Hence, proved.