(3-cot300)=tan3600-2sin600
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°
[
]
= 3√3 - √3
= 2√3
∴ L.H.S = R.H.S
Hence, proved.
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