Question

If \( \lim_{x \to 0} \frac{1 - \cos(\alpha x)\cos((\alpha + 1)x)\cos((\alpha + 2)x)}{\sin^2((\alpha + 1)x)} = 2 \), then the product of all possible values of \( \alpha \) is:

• A. 1
• B. -1
• C. 2
• D. -2

Hint:

For limits involving \( 1 - \cos(ax)\cos(bx)\dots \), the expansion shortcut \( \frac{a^2 + b^2 + \dots}{2} \) is much faster than applying L'Hôpital's Rule multiple times.

Answer 1

The Correct Option is B