Maths-
General
Easy

Question

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

  1. 3
  2. 5
  3. 7
  4. none of these

hintHint:

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+straight pi over 4, where n is any integer
    hence solution in the given interval is,
    x = straight pi over 4 b, 1 + straight pi over 4 2+ straight pi over 4, 3 + straight pi over 4, 4+straight pi over 4, 5 + straight pi over 4
    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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