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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If f x = t a n - 1 2 x 1 + 2 2 x + 1 , then ∑ r = 0 9 f r is

Options

  1. Atan - 1 ⁡ 1024
  2. Btan - 1 ⁡ 1023 1024
  3. Ctan - 1 ⁡ 1023 1025
  4. DNone of these

Correct answer

C. tan - 1 ⁡ 1023 1025

Step-by-step solution

Let, y = t a n - 1 2 x + 1 - 2 x 1 + 2 x ⋅ 2 x + 1 = tan - 1 ⁡ 2 x + 1 - tan - 1 ⁡ 2 x ∑ r = 0 9 f r = tan - 1 ⁡ 2 10 - tan - 1 ⁡ 1 = tan - 1 ⁡ 1023 1025

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