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AP EAMCET202423 May 2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

aligned & ^2 18^ + ^2 24^ + ^2 36^ + ^2 42^ + ^2 78^ + & ^2 90^ + ^2 96^ + ^2 102^ + ^2 138^ + ^2 162^ = aligned

Options

  1. A11 2
  2. B9 2
  3. C5
  4. D4

Correct answer

A. 11 2

Step-by-step solution

aligned & array r Since, ^2 18^ + ^2 24^ + ^2 36^ + ^2 42^ + ^2 78^ + ^2 90^ + ^2 96^ + ^2(180-78)^ + ^2(180-42)^ + ^2(180-18)^ =1+2 ^2 18^ + ^2 36^ + ^2 24^ + ^2 96^ +2 ^2 42^ +2 ^2 78^ array & + 1- 192^ 2 +1- 84^ +1- 15^ & =1+2 ( 5 -1 4 )^2+ 10-2 5 16 + 1- 48^ 2 & ( 84^ - 24^ ) & =3+ 2(5+1-2 5 ) 16 + 5- 5 8 + 1 2 - 1 2 48^ & - 1 2 (180^ +12^ )+ 1 2 - 84^ - (180^ -24^ ) & =4+ 6-2 5 8 + 5 5 8 - 1 2 ( 48^ - 12^ )- & (-2 54^ 30^ ) & =4+ 11-3 5 8 - 1 2 (-2 30^ 18^ )- & =4+ 11-3 5 8 + 5 -1 8 + 5 +1 4 =4+ 3 2 = 11 2 . a

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