Trigonometric Equations Question 350
Question: If $ \frac{1-{{\tan }^{2}}\theta }{{{\sec }^{2}}\theta }=\frac{1}{2} $ , then the general value of $ \theta $ is
Options:
A) $ n\pi \pm \frac{\pi }{6} $
B) $ n\pi +\frac{\pi }{6} $
C) $ 2n\pi \pm \frac{\pi }{6} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \frac{1-{{\tan }^{2}}\theta }{{{\sec }^{2}}\theta }=\frac{1}{2}\Rightarrow {{\cos }^{2}}\theta -{{\sin }^{2}}\theta =\frac{1}{2} $
$ \Rightarrow $ $ \cos 2\theta =\frac{1}{2}=\cos ( \frac{\pi }{3} ) $
$ \Rightarrow $ $ 2\theta =2n\pi \pm \frac{\pi }{3}\Rightarrow \theta =n\pi \pm \frac{\pi }{6} $ .
BETA
