Question

Total number of solutions of sin{x} = cos{x}, where {.} denotes the fractional part, in [0, 2] is equal to

- 3
- 5
- 7
- none of these

Hint:

### In this question we have given, sin{x} = cos{x}. It the fractional part. We know that {x} = x – [x]. And its region is [ 0, 2 π ]. It always in the 0 < {x} < 1.

## The correct answer is: 7

### Here, we have to find the number of solutions

Firstly, we have given,

Sin{x} = cos{x}

Tan{x} = 1

Thus, the general solution is

{x}=x−[x]=nπ+, where n is any integer

hence solution in the given interval is,

x = b, 1 + 2+ , 3 + , 4+, 5 +

Therefore, the number of solutions is 6

The correct answer is 6.

In this question, we have to find the number of solutions. Here we have fractional part of x. It is {x} and {x}= x-[x]. The {x} is always belongs to 0 to 1.

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