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AP EAMCET202120 Aug 2021Evening ShiftMathematicsProperties of TrianglesActual

What is the value of ( a - b ) 2 cos 2 c 2 + ( a + b ) 2 sin 2 c 2 =

Options

  1. Ac 2
  2. Ba 2 + b 2
  3. Ca 2 + b 2 + c 2
  4. Da 2 - b 2 + c 2

Correct answer

A. c 2

Step-by-step solution

Given that: ( a - b ) 2 cos 2 c 2 + ( a + b ) 2 sin 2 c 2 = ( a 2 - 2 a b + b 2 ) cos 2 c 2 + ( a 2 + 2 a b + b 2 ) sin 2 c 2 = ( a 2 + b 2 ) ( cos 2 c 2 + sin 2 c 2 ) + 2 a b ( sin 2 c 2 - cos 2 c 2 ) As we know that cos 2 A = cos 2 A - sin 2 A = ( a 2 + b 2 ) - 2 a b cos C As we know that cos C = a 2 + b 2 - c 2 2 a b = ( a 2 + b 2 ) - 2 a b ( a 2 + b 2 - c 2 2 a b ) = c 2

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