Question

If \( \tan \frac{\pi}{18}, x \) and \( \tan \frac{\pi}{18} \) are in AP and \( \tan \frac{5\pi}{18} \) are in AP, then the value of \( \frac{x}{y} \) will be

• A. \( \frac{1}{2} \)
• B. 2
• C. 1
• D. \( \frac{1}{4} \)

Hint:

When solving AP problems involving trigonometric functions, use the common difference property of AP to find relations between terms.

Answer 1

The Correct Option is B

The tangent of angles forms an arithmetic progression (AP) as given. Therefore, solving the equations based on tangent properties results in the ratio \( \frac{x}{y} = 2 \).