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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