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JEE Main20266 April 2026Morning ShiftMathematicsTrigonometric EquationsActual

Let S = (-2 , 2 ) : + 1 = 3 . Then _ S is equal to:

Options

  1. A- 2 3
  2. B- 4 3
  3. C2 3
  4. D4 3

Correct answer

B. - 4 3

Step-by-step solution

Given equation: + 1 = 3 Using half-angle formulas, we get: 2 ^2 2 = 2 3 2 2 2 2 ( 2 - 3 2 ) = 0 This gives two cases: Case 1: 2 = 0 2 = (2k+1) 2 = (2k+1) Since (-2 , 2 ) , the possible values are = - , . Case 2: 2 - 3 2 = 0 2 = 1 3 2 = k + 6 = 2k + 3 Since (-2 , 2 ) , the possible values are: For k = 0 , = 3 For k = -1 , = -2 + 3 = - 5 3 Thus, the set of solutions is S = - , , 3 , - 5 3 . Sum of all solutions in S : _ S = - + + 3 - 5 3 = - 4 3 Answer: - 4 3

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