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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Trigonometry

JEE Advanced · Mathematics · Trigonometry

If f(x)=(3)/(1+ ^2 x)+(9)/(1+ ^2 x) , then :

If f(x)=31+tan⁡2x+91+cot⁡2xf(x)=\frac{3}{1+\tan ^2 x}+\frac{9}{1+\cot ^2 x}, then :

Options

  1. Anumber of integers in the range of f(x)f(x) is 7 .
  2. Bnumber of integers in the range of f(x)f(x) is 5 .
  3. Csum of the integers in the range of f(x)f(x) is 30 .
  4. Dsum of the integers in the range of f(x)f(x) is 42 .

Correct answer

C. sum of the integers in the range of f(x)f(x) is 30 .

Step-by-step solution

f(x)=3cos⁡2x+9sin⁡2x,x≠nπ2,n∈I=3+6sin⁡2xf(x)=3 \cos ^2 x+9 \sin ^2 x, x \neq \frac{n \pi}{2}, n \in I=3+6 \sin ^2 x Range of f(x)=(3,9)f(x)=(3,9)
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