Question

If \( \theta \) is an acute angle, \( x = \sum_{n=0}^{\infty} \cos^{2n} \theta \), \( y = \sum_{n=0}^{\infty} \sin^{2n} \theta \), then \( \frac{1}{x^2} + \frac{1}{y^2} = \)

• A. \( 1 - \frac{2}{xy} \)
• B. \( 1 - \frac{1}{xy} \)
• C. \( 1 + \frac{1}{xy} \)
• D. \( 1 + \frac{2}{xy} \)

Hint:

For these variables, \( x+y = xy \) is a very useful property. From this, it follows that \( 1/x + 1/y = 1 \). Recognizing these patterns quickly simplifies complex algebraic manipulations.

Answer 1

The Correct Option is A