Trigonometric Identities Question 47
Question: If $ x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3} $ , then $ xy+yz+zx= $
[EAMCET 1994]
Options:
A) -1
B) 0
C) 1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3} $
$ \Rightarrow \frac{x}{1}=\frac{y}{-2}=\frac{z}{-2}=\lambda $ (say)
$ \Rightarrow x=\lambda ,\ y=-2\lambda ,,z=-2\lambda $
$ \therefore xy+yz+zx=-2{{\lambda }^{2}}+4{{\lambda }^{2}}-2{{\lambda }^{2}}=0 $ .
BETA
