Trigonometric Identities Question 267
Question: The number of solutions of the equation $ \sin ( \frac{\pi x}{2\sqrt{3}} )=x^{2}-2\sqrt{3}x+4 $
Options:
A) forms an empty set
B) is only one
C) is only two
D) is more than 2
Show Answer
Answer:
Correct Answer: B
Solution:
$ \sin ( \frac{\pi x}{2\sqrt{3}} )=x^{2}-2\sqrt{3}x+4={{(x-\sqrt{3})}^{2}}+1 $ $ \because $ $ RHS\ge 1 $ so, the solution exists If and only if $ x-\sqrt{3}=0\Rightarrow x=\sqrt{3} $ and then equation is obviously satisfied
BETA
