Question

$cos 20^{\circ} + cos 80^{\circ} - \sqrt{3} cos 50^{\circ} =$

• A. -1
• B. 0
• C. 1
• D. $\sqrt{3}$

Hint:

Look for angles that sum or subtract to standard values ($30^{\circ}, 45^{\circ}, 60^{\circ}$) when using transformation formulas.

Answer 1

The Correct Option is B

Step 1: Concept
Use the sum-to-product formula: $cos C + cos D = 2 cos(\frac{C+D}{2}) cos(\frac{C-D}{2})$.

Step 2: Meaning
$cos 80^{\circ} + cos 20^{\circ} = 2 cos 50^{\circ} cos 30^{\circ}$.

Step 3: Analysis
Substitute the value of $cos 30^{\circ} = \sqrt{3}/2$. So, $2 cos 50^{\circ} (\sqrt{3}/2) = \sqrt{3} cos 50^{\circ}$.

Step 4: Conclusion
The expression becomes $\sqrt{3} cos 50^{\circ} - \sqrt{3} cos 50^{\circ} = 0$. Final Answer: (B)