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JEE Main202131 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

The number of solutions of the equation 32 tan 2 x + 32 sec 2 x = 81 , 0 ≤ x ≤ π 4 is :

Options

  1. A0
  2. B2
  3. C1
  4. D3

Correct answer

C. 1

Step-by-step solution

Given, 32 tan 2 x + 32 sec 2 x = 81 ,           0 ≤ x ≤ π 4 32 tan 2 x + 32 1 + tan 2 x = 81 32 tan 2 x + 32 . 32 tan 2 x = 81 33 × 32 tan 2 x = 81 32 tan 2 x = 27 11 tan 2 x = ln 32 27 11 tan x = ln 32 27 11 ∈ 0 , 1 One solution in 0 , π 4

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