Number of solution of the equation | cos x | = 2 [ x ] are (where | x | , [ x ] are modulus and greatest integer function respectively).

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Number of solution of the equation

| \cos x | = 2 [x]

are (where

| x |, [x]

are modulus and greatest integer function respectively).

MathematicsFunctionsBITSATBITSAT 2019

Options:

A $0$
B $2$
C $1$
D infinitely many

Solution:

2051 Upvotes Verified Answer

The correct answer is:

0

Given, $| \cos x | = 2 [x]$

$0 \leq | \cos x | \leq 1$

$∴ 0 \leq 2 [x] \leq 1$

$0 \leq [x] \leq \frac{1}{2}$

$[x] = 0$

$\Rightarrow x \in [0, 1)$

But $| \cos x | = 0$

$\Rightarrow x = n π + \frac{π}{2}$ for any value of $n \in Z$

Hence, the equation has no solution.

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