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AP EAMCET202423 May 2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

aligned ^2 16 + ^2 2 16 + ^2 & 3 16 + ^2 4 16 & + ^2 5 16 + ^2 6 16 + ^2 7 16 = aligned

Options

  1. A35
  2. B41
  3. C37
  4. D33

Correct answer

A. 35

Step-by-step solution

Let, aligned & K= ^2 16 + ^2 2 16 + ^2 3 16 + .+ ^2 7 16 & = ^2 16 + ^2 ( 2 - 16 ) + ^2 ( 8 )+ ^2 ( 2 - 8 ) & + ^2 3 2 + ^2 ( 2 - 3 16 ) + ^2 4 aligned aligned = ( ^2 16 + ^2 16 )+ ( ^2 . & . 8 + ^2 8 ) & + ( ^2 3 16 + ^2 3 16 )+1 aligned Now, ( ^2 16 + ^2 16 )= ( 16 + 16 )^2-2= ( ^2 16 + ^2 16 16 16 )^2-2= 4 ^2 8 -2= 8 2 ^2 8 -2= 8 1- 4 -2= 8 2 2 -1 -2=8 2 ( 2 +1)-2 ...(i) Similarly, ^2 8 + ^2 8 = 8 1- 2 -2=6 ...(ii) and ^2 3 16 + ^2 3 16 = 8 1- 3 4 -2=8 2 ( 2 -1)-2 ...(iii) So, by equation (i), (ii) and (iii), we

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