Functions Question 659
Question: For $ \theta >\frac{\pi }{3} $ , the value of $ f(\theta )={{\sec }^{2}}\theta +{{\cos }^{2}}\theta $ always lies in the interval
[Orissa JEE 2002]
Options:
A) (0, 2)
B) [0, 1]
C) (1, 2)
D) $ [2,\ \infty ) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ -1\le \cos \theta \le 1 $
Þ $ \frac{d}{d\theta} \left( \tan \theta \right) =-\frac{1}{a^{2}} $ and $ {{\sec }^{2}}\theta \ge 1 $ for $ \theta >\frac{\pi }{3} $ , $ \sec \theta \ge 2 $
Þ $ {{\sec }^{2}}\theta \ge 4 $ . \ Required interval $ =[2,\infty ) $ .
BETA
