Question

The value of \( \cos 1^\circ \cos 2^\circ \dots \cos 100^\circ \) is:

• A. 1
• B. -1
• C. 0
• D. 1/2

Hint:

In a long product of trigonometric functions, always look for specific values like $\sin 0^{\circ}$, $\cos 90^{\circ}$, or $\tan 0^{\circ}$.

Answer 1

The Correct Option is C

Step 1: Concept
Check if any of the terms in the product equals zero.
Step 2: Analysis
The sequence includes $\cos 1^{\circ}, \cos 2^{\circ}, \dots, \cos 90^{\circ}, \dots, \cos 100^{\circ}$.
We know $\cos 90^{\circ} = 0$.
Step 3: Conclusion
Since one term is zero, the entire product is zero.
Final Answer: (C)