Trigonometric Identities Question 33
Question: $ \cos 2\theta +2\cos \theta $ is always
Options:
A) Greater than $ -\frac{3}{2} $
B) Less than or equal to $ \frac{3}{2} $
C) Greater than or equal to $ -\frac{3}{2} $ and less than or equal to 3
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ \cos 2\theta +2\cos \theta =2{{\cos }^{2}}\theta -1+2\cos \theta $ $ =2{{( \cos \theta +\frac{1}{2} )}^{2}}-\frac{3}{2} $ Now $ 2{{( \cos \theta +\frac{1}{2} )}^{2}}\ge 0 $ for all $ \theta $
$ \therefore 2{{( \cos \theta +\frac{1}{2} )}^{2}}-\frac{3}{2}\ge \frac{-3}{2} $ for all $ \theta $ .
Þ $ \cos 2\theta +2\cos \theta \ge \frac{-3}{2} $ for all $ \theta $
BETA
