Question

If \(x = \frac{1 + \cos 2\theta}{\tan \theta - \sec \theta}\) and \(y = \frac{\tan \theta + \sec \theta}{\sec^2 \theta}\), then \(\frac{y}{x}\) is equal to:

• A. $\dfrac{1}{2}$
• B. $2$
• C. $-2$
• D. $-\dfrac{1}{2}$
• E. $1$

Hint:

When simplifying trigonometric expressions, always convert everything to $\sin$ and $\cos$ first. Use $1 + \cos 2\theta = 2\cos^2\theta$ and $\sin^2\theta - 1 = -\cos^2\theta$ to cancel terms cleanly.

Answer 1

The Correct Option is D