Trigonometric Identities Question 262
Question: The solution set of the system of equation $ x+y=2\pi /3, $ $ \cos x+\cos y=3/2, $ where x and y are real, is
Options:
A) $ x=\frac{\pi }{3}-n\pi ,y=n\pi $
B) $ \phi $
C) $ x=n\pi ,y=\frac{\pi }{3}-n\pi $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \cos x+\cos y=\frac{3}{2} $
$ \Rightarrow 2\cos ( \frac{x+y}{2} )\cos ( \frac{x-y}{2} )=\frac{3}{2} $
$ \Rightarrow \cos ( \frac{x-y}{2} )=\frac{3}{2}( \because x+y=\frac{2\pi }{3} ) $ Which is not possible (as $ \cos \theta \le 1 $ ) Thus, the solution set is a null set.
BETA
