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AP EAMCET20224 Jul 2022Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If 4 + 6 e 2 x + 1 tan h x = 11 cos h x + 11 sin h x , then x =

Options

  1. Alog e 10
  2. Blog e 4
  3. Clog e 5
  4. Dlog e 2

Correct answer

D. log e 2

Step-by-step solution

Given: 4 + 6 e 2 x + 1 tan h x = 11 cos h x + 11 sin h x ⇒ 4 + 6 e 2 x + 1 e x - e - x e x + e - x = 11 e x + e - x 2 + 11 e x - e - x 2 ⇒ 4 + 6 e 2 x + 1 e 2 x - 1 e 2 x + 1 = 11 e x ⇒ 4 + 6 e 2 x - 1 = 11 e x ⇒ 6 e 2 x - 11 e x - 2 = 0 Put e x = t ;   t > 0 ⇒ 6 t 2 - 11 t - 2 = 0 ⇒ t = 11 ± 121 + 48 12 ⇒ t = 2 ,   - 1 6 Since, t > 0 , so t = 2 ⇒ e x = 2 ⇒ x log e e = log e 2 ⇒ x = log e 2

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