The number of solutions of the equation $| cos x | = 2 [x]$ are (where $[.]$ denotes the greatest integer function) is/are

0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $0$
$2 [x]$ always takes even integral values.
$\Rightarrow - 2 > 2 [x] > 2$ and $[x] = 0$
And, $0 \leq | cos x | \leq 1$
Therefore, only possible intersection of their ranges is $0$
$| cos x | = 0$ occurs at $x = (2 n - 1) \frac{π}{2}$ for which $[x] \neq 0$
Hence, no solution exists.

Suggest Corrections

Similar questions

| cos x | = 2 [x]

[]

[sin x] = cos x \forall x \in [0, 2 π]

[]

[3 x] - [x + 1] = 3 x

[.]

The number of solutions of equation [sin x ] = [1 + sin x] + [ 1 - cos x] where [.] denotes the greatest integer function and is

cos [x] = e^{2 x - 1}, x \in [0, 2 π],

[.]

Join BYJU'S Learning Program