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The value of l i m x → 0 1 - c o s 3 sin ⁡ x sin ⁡ x s i n sin ⁡ x c o s sin ⁡ x is equal to

Options

  1. A3 2
  2. B1
  3. C0
  4. D2

Correct answer

A. 3 2

Step-by-step solution

Let, sin ⁡ x = t ⇒ l i m t → 0   1 - c o s 3 t t sin ⁡ t cos ⁡ t ⇒ l i m t → 0 1 - cos ⁡ t t 2 × t sin ⁡ t × 1 + cos ⁡ t + cos 2 ⁡ t cos ⁡ t ⇒ 1 2 × 1 × 1 + 1 + 1 1 = 3 2

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