Question

If \( x \cos \theta = 1 \), \( \tan \theta = y \), then the value of \( x^2 - y^2 \) is:

• A. \( 2 \)
• B. \( 0 \)
• C. \( -2 \)
• D. \( 1 \)

Hint:

Using Pythagoras identity: \[ \sin^2 \theta + \cos^2 \theta = 1 \] helps in solving such expressions.

Answer 1

The Correct Option is D

Given:
\[ x = \frac{1}{\cos \theta}, \quad y = \tan \theta = \frac{\sin \theta}{\cos \theta} \] We need to find:
\[ x^2 - y^2 \] Substituting:
\[ \frac{1}{\cos^2 \theta} - \frac{\sin^2 \theta}{\cos^2 \theta} \] \[ = \frac{1 - \sin^2 \theta}{\cos^2 \theta} = \frac{\cos^2 \theta}{\cos^2 \theta} = 1 \]