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:

For collinearity: \begin{itemize} \item Compare slopes. \item Trig coordinates often reduce to angle identities. \end{itemize}

Answer 1

The Correct Option is D