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√3 sin A = Cos A
√3 = cos A/sin A
√3 = Cot A
therefore, Angle A = 30°
Now, substituting the value of A in the given equation we get :-
= 3 cos²30°+ 2 cos 30°/ 3 cos 30° + 2
= 3(√3/2)² + 2 (√3/2) / 3(√3/2) + 2
= 9/4 + √3 / 3√3/2 + 2
= 9+4√3/4 / 3√3 + 4/2
= √3/2
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