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MHT CET202520 Apr 2025Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If 3 2 =2 3 and 0 < < , then the value of is equal to

Options

  1. A17 4
  2. B5 2 4
  3. C3 2 4
  4. D15 4

Correct answer

D. 15 4

Step-by-step solution

Given the equation 3 2 = 2 3 , apply the double and triple angle formulas to obtain 6 = 6 - 8 ^3 . Divide both sides by (since 0 for 0 Substitute ^2 = 1 - ^2 to form a quadratic in : 6 = 6 - 8(1 - ^2 ) , which simplifies to 4 ^2 - 3 - 1 = 0 . Factor as (4 + 1)( - 1) = 0 , giving = - 1 4 or = 1 . Only = - 1 4 lies within the domain 0 Using ^2 = 1 - ^2 , compute ^2 = 1 - (- 1 4 )^2 = 15 16 . Since > 0 in this interval, = 15 4 . The correct option is D .

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