Trigonometric Equations Question 344
Question: If $ 1+\cot \theta =cosec\theta $ , then the general value of $ \theta $ is
[Roorkee 1981]
Options:
A) $ n\pi +\frac{\pi }{2} $
B) $ 2n\pi -\frac{\pi }{2} $
C) $ 2n\pi +\frac{\pi }{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \frac{1}{\sin \theta }=1+\frac{\cos \theta }{\sin \theta }\Rightarrow \sin \theta +\cos \theta =1 $
$ \Rightarrow $ $ \cos ( \theta -\frac{\pi }{4} ),=\cos \frac{\pi }{4}\Rightarrow \theta -\frac{\pi }{4}=2n\pi \pm \frac{\pi }{4} $ Hence $ \theta =2n\pi $ or $ \theta =2n\pi +\frac{\pi }{2} $ . But $ \theta =2n\pi $ is ruled out.
BETA
