Question

prove √3+1 (3-cot30) =3 tan60-2sin 60
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Answer 1

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.