Verified Solution • 2025–26 Session moderate

QJEEM25Madbda: JEE Main 2025 Mathematics - Class 11 JEEM25Madbda Solution: Let the range of the function be . Then the distance of the…

Let the range of the function f(x)=6+16cos⁡x⋅cos⁡(π3−x)⋅cos⁡(π3+x)⋅sin⁡3x⋅cos⁡6x,x∈Rf(x)=6+16 \cos x \cdot \cos \left(\frac{\pi}{3}-x\right) \cdot \cos \left(\frac{\pi}{3}+x\right) \cdot \sin 3 x \cdot \cos 6 x, x \in \mathbf{R} be [α,β][\alpha, \beta] . Then the distance of the point (α,β)(\alpha, \beta) from the line 3x+4y+12=03 x+4 y+12=0 is :

Multiple Choice Options

  • A 11
  • B 10
  • C 8
  • D 9

Step-by-Step Verified Solution

f(x)=6+16(14cos⁡3x)sin⁡3x⋅cos⁡6x=6+4cos⁡3xsin⁡3xcos⁡6x=6+sin⁡12x Range of f(x) is [5, 7] (α,β)≡(5,7) distance =|15+28+125|=11

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