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MHT CET202525 Apr 2025Morning ShiftMathematicsTrigonometric EquationsActual

The principal solution of (5+3 )(2 +1)=0 are

Options

  1. A- 3 , 2 3
  2. B2 3 , 5 3
  3. C2 3 , 4 3
  4. D2 3 , 7 3

Correct answer

C. 2 3 , 4 3

Step-by-step solution

Principal solutions of (5+3 )(2 +1)=0 The equation factors into two cases. Since 5+3 = 0 gives = - 5 3 , which lies outside the range [-1,1] , this case yields no solutions. For 2 +1 = 0 , we solve = - 1 2 . In the interval [0,2 ) , cosine is negative in quadrants II and III. Using the reference angle = 3 , the solutions are = - = 2 3 and = + = 4 3 . Among the given options, only option C provides these solutions: 2 3 and 4 3 . Final answer: C

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