Trigonometric Equations Question 80
Question: $ \cot \theta =\sin 2\theta (\theta \ne n\pi $ , n is integer), if $ \theta = $
[BIT Ranchi 1991; Pb. CET 1991]
Options:
A) $ 45^{o} $ and $ 60^{o} $
B) $ 45^{o} $ and $ 90^{o} $
C) $ 45^{o} $ only
D) $ 90^{o} $ only
Show Answer
Answer:
Correct Answer: B
Solution:
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$ \cot \theta =\sin 2\theta ,\text{ }(\theta \ne n\pi )\Rightarrow 2{{\sin }^{2}}\theta \cos \theta =\cos \theta $
$ \Rightarrow $ $ \cos \theta =0 $ or $ {{\sin }^{2}}\theta =\frac{1}{2}={{\sin }^{2}}( \frac{\pi }{4} ) $
$ \Rightarrow $ $ \theta =(2n+1)\frac{\pi }{2} $ or $ \theta =n\pi \pm \frac{\pi }{4} $
$ \Rightarrow $ $ \theta =90^{o} $ and $ 45^{o} $ .
BETA
