Trigonometric Equations Question 352
Question: If $ \cos \theta +\sec \theta =\frac{5}{2} $ , then the general value of $ \theta $ is
Options:
A) $ n\pi \pm \frac{\pi }{3} $
B) $ 2n\pi \pm \frac{\pi }{6} $
C) $ n\pi \pm \frac{\pi }{6} $
D) $ 2n\pi \pm \frac{\pi }{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ {{\cos }^{2}}\theta -\frac{5}{2}\cos \theta +1=0 $
$ \Rightarrow $ $ \cos \theta =\frac{(5/2)\pm \sqrt{(25/4)-4}}{2}=\frac{5\pm 3}{4} $ Rejecting (+) sign,
$ \Rightarrow $ $ \cos \theta =\frac{1}{2}=\cos ( \frac{\pi }{3} )\Rightarrow \theta =2n\pi \pm \frac{\pi }{3} $ .
BETA
