Trigonometric Equations Question 94
Question: If n is any integer, then the general solution of the equation $ \cos x-\sin x=\frac{1}{\sqrt{2}} $ is
[J & K 2005]
Options:
A) $ x=2n\pi -\frac{\pi }{12} $ or $ x=2n\pi +\frac{7\pi }{12} $
B) $ x=n\pi \pm \frac{\pi }{12} $
C) $ x=2n\pi +\frac{\pi }{12} $ or $ x=2n\pi -\frac{7\pi }{12} $
D) $ x=n\pi +\frac{\pi }{12} $ or $ x=n\pi -\frac{7\pi }{12} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given equation is, $ \cos x-\sin x=\frac{1}{\sqrt{2}} $ Dividing equation by $ \sqrt{2} $ , $ \frac{1}{\sqrt{2}}\cos x-\frac{1}{\sqrt{2}}\sin x=\frac{1}{2} $ $ \cos ( \frac{\pi }{4}+x )=\cos \frac{\pi }{3} $ . Hence, $ \frac{\pi }{4}+x=2n\pi \pm \frac{\pi }{3} $ $ x=2n\pi +\frac{\pi }{3}-\frac{\pi }{4}=2n\pi +\frac{\pi }{12} $ or $ x=2n\pi -\frac{\pi }{3}-\frac{\pi }{4}=2n\pi -\frac{7\pi }{12} $ .
BETA
