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MHT CET202615 April 2026Morning ShiftMathematicsTrigonometric EquationsActual

If (p ) + (q ) = 0 and p q , then the general value of (where n is any integer) is...

Options

  1. A(3n+1) p - q
  2. B(2n+1) p q
  3. C(n 1) p q
  4. D(n+2) p + q

Correct answer

B. (2n+1) p q

Step-by-step solution

Given (p ) + (q ) = 0 Using the formula C + D = 2 ( C+D 2 ) ( C-D 2 ) : 2 ( p+q 2 ) ( p-q 2 ) = 0 This implies either ( p+q 2 ) = 0 or ( p-q 2 ) = 0 If ( p+q 2 ) = 0 , then p+q 2 = (2n+1) 2 , where n is an integer. = (2n+1) p+q If ( p-q 2 ) = 0 , then p-q 2 = (2n+1) 2 , where n is an integer. = (2n+1) p-q Combining both cases, the general value of is (2n+1) p q Answer: (2n+1) p q

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