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MHT CET20255 May 2025Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

aligned & If ( + )=1, ( - )= 1 2 , , [0, 2 ] & then ( +2 ) (2 + )= aligned

Options

  1. A1
  2. B-1
  3. C0
  4. D4

Correct answer

A. 1

Step-by-step solution

Given: ( + )=1 and ( - )= 1 2 , with , [0, 2 ] . From ( + )=1 , and since + [0, ] , the only angle satisfying this is + = 2 . Similarly, ( - )= 1 2 with - [- 2 , 2 ] gives - = 6 . Solving the system: + = 2 - = 6 Adding yields 2 = 2 3 , so = 3 . Substituting gives = 2 - 3 = 6 . Now compute ( +2 ) = ( 2 3 ) = - 3 and (2 + ) = ( 5 6 ) = - 1 3 . The product is (- 3 ) (- 1 3 ) = 1 .

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