- Thread starter
- Admin
- #1
- Feb 14, 2012
- 3,965
Find all \(\displaystyle x\) in the interval \(\displaystyle [0, 2\pi] \) which satisfies \(\displaystyle 2\cos(x) \le \left|\sqrt{1+\sin (2x)}-\sqrt{1-\sin (2x)} \right|\le \sqrt{2}\)
If correct, the problem is set up as 'non challenge question' because the requirement is reduced to...Find all \(\displaystyle x\) in the interval \(\displaystyle [0, 2\pi] \) which satisfy \(\displaystyle 2\cos x \le |\sqrt{1+\sin (2x)}-\sqrt{1-\sin (2x)}|\le \sqrt{2}\)
one solution cos x <= 0Find all \(\displaystyle x\) in the interval \(\displaystyle [0, 2\pi] \) which satisfies \(\displaystyle 2\cos(x) \le \left|\sqrt{1+\sin (2x)}-\sqrt{1-\sin (2x)} \right|\le \sqrt{2}\)
Squaring the expression in the middle gives:Find all \(\displaystyle x\) in the interval \(\displaystyle [0, 2\pi] \) which satisfies \(\displaystyle 2\cos(x) \le \left|\sqrt{1+\sin (2x)}-\sqrt{1-\sin (2x)} \right|\le \sqrt{2}\)