Question

Consider three points \( P(\cos \alpha, \sin \beta) \), \( Q(\sin \alpha, \cos \beta) \) and \( R(0, 0) \), where \( 0<\alpha, \beta<\frac{\pi}{4} \). Then:

• A. \( P \) lies on the line segment \( RQ \).
• B. \( Q \) lies on the line segment \( PR \).
• C. \( R \) lies on the line segment \( PQ \).
• D. \( P, Q, R \) are non-collinear.

Hint:

To check collinearity, use the area formula with coordinates. A zero area indicates collinearity, while a non-zero area shows the points are non-collinear.