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JEE Main202226 Jul 2022Evening ShiftMathematicsDifferentiationActual

The value of log e 2 d dx log cos x cosec x at x = π 4 is

Options

  1. A- 2 2
  2. B2 2
  3. C- 4
  4. D4

Correct answer

D. 4

Step-by-step solution

For log e 2 d d x log cos x cosec x let, y = log cos x cosec x i.e. y = - ln sin x ln cos x ⇒ d y d x = - cot x · ln cos x + tan x · ln sin x ln cos x 2 Now d y d x x = π 4 = - cot π 4 · ln cos π 4 + tan π 4 · ln sin π 4 ln cos π 4 2 = 4 ln 2 ⇒ log e 2 · 4 ln 2 = 4

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