Question

Choose the most appropriate options. Let \( P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \} \) and \( Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \} \). Then,

• A. \( P \subset Q \) and \( Q - P \neq \emptyset \)
• B. \( Q \not\subset P \)
• C. \( P \not\subset Q \)
• D. \( P = Q \)

Hint:

Always check the conditions for the set relationships before concluding about inclusion or equality.

Answer 1

The Correct Option is D

After solving the equations for \( P \) and \( Q \), we find that both sets are equivalent. Hence, \( P = Q \).