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AP EAMCET202124 Aug 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If + = , then what is the value of ^2 + ^2 + ^2 is equal to

Options

  1. A1+2 ^3 ^3 ^3
  2. B1+2 ^2 ^2 ^2
  3. C1+2
  4. D1+4

Correct answer

C. 1+2

Step-by-step solution

aligned & Given, + = & Then, ^2 + ^2 + ^2 & = 1 2 [2 ^2 +2 ^2 +2 ^2 ] & = 1 2 [1+ 2 +1+ 2 +2 ^2 ] & [ 2 ^2 A=1+ 2 A ] & = 1 2 [2+ 2 + 2 +2 ^2 ] & = 1 2 [2+2 ( 2 +2 2 ) ( 2 -2 2 )+2 ^2 ] & = 1 2 [2+2 ( 2( ) 2 ) ( - )+2 ^2 ] aligned aligned & = 1 2 [2+2 ( - )+2 ^2 ] & =1+ ( - )+ ^2 & =1+ ( - )+ & =1+ 2 ( - + 2 ) ( - - 2 ) & =1+2 ( - + + 2 ) ( - - - 2 ) & =1+2 ( 2 2 ) (- 2 2 ) & =1+2 (- ) & =1+2 & [ (- )= ] aligned

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