1. Prove that (13 + 1) (3 - cot 30°) = tan 3 60° - 2 sin 60°.
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Answer:
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° Since, tan 60o = √3 and sin 60o = √3/2, We get, (√3)3 – 2.(√3/2) = 3√3 – √3 = 2√3
Therefore,
L.H.S = R.H.S
Hence, proved
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