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MHT CET202521 Apr 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

3 ^6 10^ -27 ^4 10^ +33 ^2 10^ =

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

Let x = 10^ and consider the triple angle formula: (3 ) = 3 - ^3 1 - 3 ^2 For = 10^ , we have 3 = 30^ and 30^ = 1 3 , so: 1 3 = 3x - x^3 1 - 3x^2 Squaring both sides to eliminate the radical: (1 - 3x^2)^2 = 3(3x - x^3)^2 Expanding both sides gives: 1 - 6x^2 + 9x^4 = 27x^2 - 18x^4 + 3x^6 Rearranging all terms to one side yields: 3x^6 - 27x^4 + 33x^2 - 1 = 0 Therefore, 3x^6 - 27x^4 + 33x^2 = 1 Final answer: 1

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