MathematicsThe function f(x)=[sinx] is not continuous at ([x] is the greatest integer less than or equal to x)

The function f(x)=[sinx] is not continuous at ([x] is the greatest integer less than or equal to x)

A
$\frac{π}{2}$
B
$π$
C
$\frac{3 π}{2}$
D
E
2 $π$

Solution:

We know f(x)=[x] is discontinuous at integral values of x.
Then, f(x)=[sinx] will be discontinuous where sinx will be integer.
Thus the solution set is, sinx=0,±1⇒x=nπ,(2n+1)

\frac{π}{2}

, where n∈I
Hence 1 is the correct option.

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