Trigonometric Equations Question 101
Question: If $ \sec 4\theta -\sec 2\theta =2 $ , then the general value of $ \theta $ is
[IIT 1963]
Options:
A) $ (2n+1)\frac{\pi }{4} $
B) $ (2n+1)\frac{\pi }{10} $
C) $ n\pi +\frac{\pi }{2} $ or $ \frac{n\pi }{5}+\frac{\pi }{10} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \sec 4\theta -\sec 2\theta =2 $
$ \Rightarrow $ $ \cos 2\theta -\cos 4\theta =-2\sin 3\theta \sin \theta $ $ \Rightarrow $ $ -\cos 4\theta =\cos (6\theta) $ $ \Rightarrow $ $ 2\cos 5\theta \cos \theta =0 $
$ \Rightarrow $ $ H=\frac{h\cot 15^{o}}{\cot 15^{o}-1} $ or $ \frac{n\pi }{5}+\frac{\pi }{10} $ .
BETA
