Trigonometric Identities Question 106
Question: If for real values of $ x,\cos \theta =x+\frac{1}{x}, $ then
[MP PET 1996]
Options:
A) $ \theta $ is an acute angle
B) $ \theta $ is a right angle
C) $ \theta $ is an obtuse angle
D) No value of $ \theta $ is possible
Show Answer
Answer:
Correct Answer: D
Solution:
The quadratic equation is $ x^{2}-x\cos \theta +1=0 $ But x is real, therefore $ B^{2}-4AC\ge 0 $
$ \Rightarrow {{\cos }^{2}}\theta \ge 4(1)(1)\Rightarrow {{\cos }^{2}}\theta \ge 4 $ , which is impossible.
BETA
