Question

For $\alpha \in \left[0, \dfrac{\pi}{2} \right]$, the angle between the lines represented by
$[x \cos\theta - y] \left[ (\cos\theta + \tan\alpha)x - (1 - \cos\theta \tan\alpha)y \right] = 0$ is

• A. $\alpha$
• B. $\theta$
• C. $\theta + \alpha$
• D. $\theta - \alpha$

Hint:

If an equation is constructed using known angle identities, match the constructed angle to its geometric interpretation.

Answer 1

The Correct Option is A

Given expression represents two lines: $x\cos\theta = y$ and $(\cos\theta + \tan\alpha)x = (1 - \cos\theta \tan\alpha)y$
From the slopes of both lines, angle between them is given as $\alpha$
Thus, by construction, $\alpha$ is the angle between the lines.