Trigonometric Equations Question 358
Question: a If $ 4{{\sin }^{2}}\theta +2(\sqrt{3}+1)\cos \theta =4+\sqrt{3} $ , then the general value of $ \theta $ is
Options:
A) $ 2n\pi \pm \frac{\pi }{3} $
B) $ 2n\pi +\frac{\pi }{4} $
C) $ n\pi \pm \frac{\pi }{3} $
D) $ n\pi -\frac{\pi }{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ 4-4{{\cos }^{2}}\theta +2,(\sqrt{3}+1)\cos \theta =4+\sqrt{3} $
$ \Rightarrow $ $ 4{{\cos }^{2}}\theta -2,(\sqrt{3}+1)\cos \theta +\sqrt{3}=0 $
$ \Rightarrow $ $ \cos \theta =\frac{2(\sqrt{3}+1)\pm \sqrt{4{{(\sqrt{3}+1)}^{2}}-16\sqrt{3}}}{8} $
$ \Rightarrow $ $ \cos \theta =\frac{\sqrt{3}}{2}\text{ or}\text{1/2}\Rightarrow \theta =2n\pi \pm \frac{\pi }{6} $ or $ 2n\pi \pm \pi /3 $ .
BETA
