Trigonometric Equations Question 381
Question: If $ \sin ( \frac{\pi }{4}\cot \theta )=\cos ( \frac{\pi }{4}\tan \theta ), $ then $ \theta = $
[Pb. CET 1988]
Options:
A) $ n\pi +\frac{\pi }{4} $
B) $ 2n\pi \pm \frac{\pi }{4} $
C) $ n\pi -\frac{\pi }{4} $
D) $ 2n\pi \pm \frac{\pi }{6} $
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Answer:
Correct Answer: A
Solution:
- We have $ \frac{\pi }{4}\cot \theta =\frac{\pi }{2}-\frac{\pi }{4}\tan \theta $
$ \Rightarrow \tan \theta +\cot \theta =2 $
$ \Rightarrow $ $ \sin 2\theta =1=\sin \frac{\pi }{2}\Rightarrow \theta =n\pi +\frac{\pi }{4} $ .
BETA
