Question

Find the number of solutions for;
[[x] - x] = sin x; where [.] denotes the greatest
integer function."​

Answer 1

Answer:

Sin x is between -1 and 1.

But [[x]-x] = [{x}] = 0 .

where {x} is fractional part of x which is can take all values between 0 and 1 including 0 but not 1

Hence Sin x = 0 is given by solution set of x = n×pi where n belongs to whole numbers.

So x ={ 0, pi , 2×pi , 3×pi ......}

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