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AP EAMCET202124 Aug 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

^2 10^ + ^2 50^ - 40^ 80^ is equal to

Options

  1. A1 4
  2. B1 2
  3. C4 3
  4. D3 4

Correct answer

D. 3 4

Step-by-step solution

aligned & ^2 10^ + ^2 50^ - 40^ 80^ & = 1 2 [2 ^2 10^ +2 ^2 50^ -2 40^ 80^ ] & = 1 2 [1+ 20^ +1+ 100^ . & .- (40^ -80^ )- (40^ +80^ ) ] & 2 ^2 A=1+ 2 A and 2 A B . & = (A-B)- (A+B) & = 1 2 [2+ 20^ + 100^ - 40^ + 120^ ] & 1 2 [2+ 20^ + 100^ - 40^ + (- 1 2 ) ] & [ (- )= , (120^ )=- 1 2 ] & aligned aligned & = 1 2 [2- 1 2 +2 ( 20+100 2 )^ ( 80 2 )^ - 40^ ] & = 1 2 [ 3 2 +2 60^ 40^ - 40^ ] & = 1 2 [ 3 2 +2 1 2 40^ - 40^ ] & = 1 2 [ 3 2 + 40^ - 40^ ]= 1 2 3 2 = 3 4 aligned

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