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If the value of l i m x → π 6 c o s x + π 3 1 - 3 tan ⁡ x is equal to λ , then the value of 120 λ 2 is equal to

Correct answer

22.5

Step-by-step solution

Let, x = π 6 - t , then l i m t → 0 c o s π 2 - t 1 - 3 t a n π 6 - t = lim t → 0 sin ⁡ t 1 - 3 1 - 3 tan ⁡ t 3 + tan ⁡ t = lim t → 0 sin ⁡ t 3 + tan t 4 tan ⁡ t = 3 4 = λ Hence, 120 λ 2 = 120 × 3 16 = 22 . 5

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