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NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If y = tan ⁡ x - sin ⁡ x , then the value of d y d x at x = 5 π 4 is

Options

  1. A2 2 + 1 2
  2. B2 2 - 1 2
  3. C2 + 1 2
  4. D2 - 1 2

Correct answer

B. 2 2 - 1 2

Step-by-step solution

In the neighbourhood of x = 5 π 4 ,   sin ⁡ x < 0 ∴   sin ⁡ x = - sin ⁡ x Now, y = tan ⁡ x - ( - sin ⁡ x ) = tan ⁡ x + sin ⁡ x Now, in the neighbourhood of x = 5 π 4 tan ⁡ x + sin ⁡ x ≃ 1 + - 1 2 , which is positive ∴ y = tan ⁡ x + sin ⁡ x Hence, d y d x = sec 2 ⁡ x + cos ⁡ x Putting x = 5 π 4 , we get, d y d x = - 2 2 - 1 2 = 2 2 - 1 2

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