Trigonometric Equations Question 83
Question: If $ \cos 40^{o}=x $ and $ \cos \theta =1-2x^{2} $ , then the possible values of $ \theta $ lying between $ 0^{o} $ and $ 360^{o} $ is
Options:
A) $ 100^{o} $ and $ 260^{o} $
B) $ 80^{o} $ and $ 280^{o} $
C) $ 280^{o} $ and $ 110^{o} $
D) $ 110^{o} $ and $ 260^{o} $
Show Answer
Answer:
Correct Answer: A
Solution:
- Here $ \cos \theta =1-2{{\cos }^{2}}40^{o} $ = $ -(2{{\cos }^{2}}40^{o}-1) $ $ =-\cos (2\times 40^{o}) $ = $ -\cos 80^{o} $ = $ \cos (180^{o}+80^{o})=\cos (180^{o}-80^{o}) $ Hence, $ \cos 260{}^\circ and\cos 100{}^\circ $ i.e., $ \theta =100{}^\circ $ and 260°.
BETA
