InterviewSolution
Saved Bookmarks
| 1. |
Solve \(\sqrt{3}\) cosx − sinx =1 |
|
Answer» We have: \(\sqrt{3 }\)cos x − sin x = 1 Dividing both sides by 2, we get cos x. \(\frac{\sqrt{3}}{2}\) − sin x . \(\frac{1}{2}\) = \(\frac{1}{2}\) ⇒ cos x . cos \(\frac{\pi}{6}\) − sin x . sin \(\frac{\pi}{6}\) = \(\frac{1}{2}\) ⇒ cos (x + \(\frac{\pi}{6}\) ) = cos ( \(\frac{\pi}{3}\) ) ⇒ x + \(\frac{\pi}{6}\) = \(2n\pi\) ± \(\frac{\pi}{3}\) ⇒ x = \(2nx\) ± \(\frac{\pi}{3}\) − \(\frac{\pi}{6}\) ⇒ x = \(2n\pi\) + \(\frac{\pi}{3}\) − \(\frac{\pi}{6}\) or x = \(2nx\) − \(\frac{\pi}{3}\) − \(\frac{\pi}{6}\) ⇒ x = \(2n\pi\) + \(\frac{\pi}{6}\) or x = \(2n\pi\) − \(\frac{\pi}{2}\) |
|