Trigonometric Equations Question 348
Question: If $ 3({{\sec }^{2}}\theta +{{\tan }^{2}}\theta )=5 $ , then the general value of $ \theta $ is
Options:
A) $ 2n\pi +\frac{\pi }{6} $
B) $ 2n\pi \pm \frac{\pi }{6} $
C) $ n\pi \pm \frac{\pi }{6} $
D) $ n\pi \pm \frac{\pi }{3} $
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Answer:
Correct Answer: C
Solution:
- $ {{\sec }^{2}}\theta +{{\tan }^{2}}\theta =\frac{5}{3} $ , also $ {{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1 $
$ \Rightarrow $ $ {{\tan }^{2}}\theta =\frac{1}{3}={{\tan }^{2}}( \frac{\pi }{6} )\Rightarrow \theta =n\pi \pm \frac{\pi }{6} $ .
BETA
