Trigonometric Equations Question 339
Question: If $ 2{{\tan }^{2}}\theta ={{\sec }^{2}}\theta , $ then the general value of $ \theta $ is
[MP PET 1989]
Options:
A) $ n\pi +\frac{\pi }{4} $
B) $ n\pi -\frac{\pi }{4} $
C) $ n\pi \pm \frac{\pi }{4} $
D) $ 2n\pi \pm \frac{\pi }{4} $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ 2{{\tan }^{2}}\theta ={{\sec }^{2}}\theta \Rightarrow 2{{\tan }^{2}}\theta ={{\tan }^{2}}\theta +1 $
$ \Rightarrow $ $ {{\tan }^{2}}\theta =1={{\tan }^{2}}( \frac{\pi }{4} )\Rightarrow \theta =n\pi \pm \frac{\pi }{4} $ .
BETA
