Sequence And Series Question 404
Question: For $ -\pi <x<\pi , $ the values of x which satisfy the relation $ {11^{1+| \cos ,x |+cos^{2}x+| {{\cos }^{3}}x |+…upt{o^{\infty }}}}=121 $ are given by
Options:
A) $ \pm \frac{\pi }{3},\pm \frac{2\pi }{3} $
B) $ \frac{\pi }{3},\frac{2\pi }{4} $
C) $ \frac{\pi }{4},\frac{3\pi }{4} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Since, $ 0<x<\pi ,-1<\cos x<1\Rightarrow 0\le |\cos x|<1 $ . We can write the given expression as $ {11^{1/(1-|\cos x|)}}=121 $
$ \Rightarrow \frac{1}{1-| \cos x |}=2 $
$ \Rightarrow 1-| \cos x |=\frac{1}{2} $
$ \Rightarrow | \cos x |=\frac{1}{2} $
$ \Rightarrow \cos x=\pm \frac{1}{2} $
$ \Rightarrow x=\pm \frac{\pi }{3},\pm \frac{2\pi }{3} $
BETA
