Functions Question 113
Question: Let $ f(\theta )=\sin \theta (\sin \theta +\sin 3\theta ) $ , then $ f(\theta ) $
[IIT Screening 2000]
Options:
A) $ \ge 0 $ only when $ \theta \ge 0 $
B) $ \le 0 $ for all real $ \theta $
C) $ \ge 0 $ for all real $ \theta $
D) $ \le 0 $ only when $ \theta \le 0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Here, $ f(\theta )=\sin \theta (\sin \theta +\sin 3\theta ) $ $ =\sin \theta (\sin \theta +3\sin \theta -4{{\sin }^{3}}\theta )=4{{\sin }^{2}}\theta (1-{{\sin }^{2}}\theta ) $ $ =4{{\sin }^{2}}\theta {{\cos }^{2}}\theta ={{(\sin 2\theta )}^{2}} $ \ $ f(\theta )\ge 0 $ for all real $ \theta $ .
BETA
