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COMEDK20269 May 2026Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The expression (x - 2 ) ( 3 2 + x ) - ^3 ( 7 2 - x ) (x - 2 ) ( 3 2 + x ) simplifies to:

Options

  1. A^2 x
  2. B1 + ^2 x
  3. C^2 x - ^2 x
  4. D-(1 + ^2 x)

Correct answer

A. ^2 x

Step-by-step solution

We simplify each term in the given expression using trigonometric identities: (x - 2 ) = - ( 2 - x ) = - x ( 3 2 + x ) = x ( 7 2 - x ) = (3 + 2 - x ) = - ( 2 - x ) = - x (x - 2 ) = ( 2 - x ) = x ( 3 2 + x ) = - x Substituting these values into the given expression: Numerator = (- x)( x) - (- x)^3 = - x + ^3 x Denominator = ( x)(- x) = - x The expression becomes: - x + ^3 x - x = 1 - ^2 x = ^2 x Answer: ^2 x

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