Q22 / 71 · NTA Abhyas (JEE Main) 2020 · Mathematics · Inverse Trigonometric Functions

If cos-1sin⁡x≥sin-1sin⁡x, then the number of integral values of x in the interval x∈0,3π are

  • A
    7
  • B
    6
  • C
    4
  • Correct answer
    D
    5

Solution

If cos-1x≥sin-1x, then x∈-12,12 {using graph}
Figure
For given inequality, we must have sin⁡x∈-12,12

⇒x∈nπ-π4,nπ+π4,n∈Ι
Possible integral values of x are 0,3,6,7,9

Hence, the correct answer is option: 'D'.

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