Trigonometric Equations Question 48
Question: If $ \sin 2\theta =\cos \theta ,0<\theta <\pi $ , then the possible values of $ \theta $ are
Options:
A) $ 90^{o},60^{o},30^{o} $
B) $ 90^{o},150^{o},60^{o} $
C) $ 90^{o},45^{o},150^{o} $
D) $ 90^{o},30^{o},150^{o} $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \sin 2\theta =\cos \theta \Rightarrow \cos \theta =\cos ( \frac{\pi }{2}-2\theta ) $
$ \Rightarrow $ $ \theta =2n\pi \pm ( \frac{\pi }{2}-2\theta )\Rightarrow \theta \pm 2\theta =2n\pi \pm \frac{\pi }{2} $ i.e., $ 3\theta =2n\pi +\frac{\pi }{2}\Rightarrow \theta =\frac{1}{3}( 2n\pi +\frac{\pi }{2} ) $ and $ -\theta =2n\pi -\frac{\pi }{2}\Rightarrow \theta =-( 2n\pi -\frac{\pi }{2} ) $ Hence value of $ \theta $ between 0 and $ \pi $ are $ \frac{\pi }{6},,\frac{\pi }{2},,\frac{5\pi }{6} $ i.e., $ 30^{o},,90^{o},,150^{o} $ .
BETA
