Trigonometric Identities Question 209
Question: The sum of all the solutions of $ \cot \theta =\sin 2\theta (\theta \ne n\pi ,n,integer) $ , $ 0\le \theta \le \pi $ is
Options:
A) $ 3\pi /2 $
B) $ \pi $
C) $ 3\pi /4 $
D) $ 2\pi $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] From the given relation $ \cos \theta =(2sin\theta cos\theta )sin\theta ,sin\theta \ne 0 $ Or $ \sin \theta =\pm \frac{1}{\sqrt{2}},or,\cos \theta =0 $ Or $ \theta =\frac{\pi }{4},\frac{3\pi }{4},\frac{\pi }{2} $ $ (\because \theta \in [0,\pi ]) $ Then the sum of roots is $ 3\pi /2 $ .
BETA
