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COMEDK202510 May 2025Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A= 3 4 , then (32 A 2 5 A 2 )=

Options

  1. A16
  2. B11
  3. C8
  4. D7

Correct answer

B. 11

Step-by-step solution

Given A = 3 4 . The expression is 32 A 2 5A 2 . Using the product-to-sum formula 2 x y = (x - y) - (x + y) , we have: 32 A 2 5A 2 = 16 2 A 2 5A 2 = 16 [ ( 5A 2 - A 2 ) - ( 5A 2 + A 2 ) ] = 16 [ (2A) - (3A) ] . Using 2A = 2 ^2 A - 1 and 3A = 4 ^3 A - 3 A : 2A = 2 ( 3 4 )^2 - 1 = 2 ( 9 16 ) - 1 = 9 8 - 1 = 1 8 . 3A = 4 ( 3 4 )^3 - 3 ( 3 4 ) = 4 ( 27 64 ) - 9 4 = 27 16 - 36 16 = - 9 16 . Substituting these values into the expression: 16 [ 1 8 - (- 9 16 ) ] = 16 [ 2 16 + 9 16 ] = 16 ( 11 16 ) = 11 . Answer: 11

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