Q40 / 83 · NTA Abhyas (JEE Main) 2020 · Mathematics · Trigonometric Equations

The number of solutions of the equation 3+cos⁡x2=4-2sin8⁡x in 0,9π is equal to

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

Solution

-1≤cos⁡x≤1⇒ 2≤3+cos⁡x≤4
⇒4≤3+cos⁡x2≤16
Also, -1≤sin⁡x≤1
⇒0≤2sin8⁡x≤2
⇒2≤4-2sin8⁡x≤4 so, equality is possible when LHS=RHS=4
⇒cos⁡x=-1 and sin⁡x=0
⇒x=(2n+1)π
⇒x=π,3π,5π,7π

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

More Trigonometric Equations Questions