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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

For x ∈ 0 , π 2 , if c o s - 1 7 2 1 + cos ⁡ 2 x + s i n 2 x - 48 c o s 2 x sin ⁡ x = x - cos - 1 k cos ⁡ x , then the value of k is equal to

Options

  1. A1
  2. B5
  3. C7
  4. D14

Correct answer

C. 7

Step-by-step solution

y = c o s - 1 7 2 1 + cos ⁡ 2 x + s i n 2   x - 48 c o s 2   x sin ⁡ x = c o s - 1 7 cos ⁡ x cos ⁡ x + 1 - 49 cos 2 x 1 - cos 2 x = c o s - 1 cos ⁡ x - c o s - 1 7 cos ⁡ x = x - c o s - 1 7 cos ⁡ x Hence, the value of k = 7

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