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MHT CET202613 April 2026Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If ( - )=a and ( - )=b , then the value of ^2( - )+2ab ( - )+ ^2( - ) is...

Options

  1. Aa^2 - 2b^2
  2. Ba^2 + 2b^2
  3. C2a^2 - b^2
  4. D2a^2 + b^2

Correct answer

D. 2a^2 + b^2

Step-by-step solution

Let x = - and y = - . Given x = a and y = b . We can write - = ( - ) - ( - ) = y - x . Using the trigonometric expansion formulas: ( - ) = (y - x) = y x + y x = a y + b x ( - ) = (y - x) = y x - y x = ab - y x Substituting these into the given expression ^2( - )+2ab ( - )+ ^2( - ) : (a y + b x)^2 + 2ab(ab - y x) + a^2 Expanding the terms, we get: a^2 ^2 y + b^2 ^2 x + 2ab y x + 2a^2b^2 - 2ab y x + a^2 Canceling 2ab y x and expressing ^2 y and ^2 x in terms of a and b : a^2(1 - ^2 y) + b^2(1 - ^2 x) + 2a^2b^2 + a^2

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