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AP EAMCET202319 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

Match the items of List - I with those of the entires of List-IIList-I aligned & (I) ^2 5^ + ^2 10^ + & ^2 15^ + + ^2 90^ = aligned aligned & (II) ^2 5^ ^2 10^ . & ^2 15^ ^2 85^ = & aligned aligned & (III) ^2 5^ + ^2 10^ & + ^2 15^ + + ^2 180^ = aligned gathered (IV) 5^ + 10^ + 15^ + .+ 175^ = gathered List-II (A) 0 (B) 19 2 (C) 18 (D) 1 (E) -1

Options

  1. A(I) - (B), (II) - (D), (III) - (C), (IV) - (A)
  2. B(I) - (B), (II) - (E), (III) - (A), (IV) - (C)
  3. C(I) - (B), (II) - (C), (III) - (A), (IV) - (D)
  4. D(I) - (C), (II) - (B), (III) - (D), (IV) - (E)

Correct answer

A. (I) - (B), (II) - (D), (III) - (C), (IV) - (A)

Step-by-step solution

aligned & array l (I) ^2 5^ + ^2 10^ + ^2 15^ + + ^2 90^ = ^2 90^ + ( ^2 5^ + ^2 85^ )+ ( ^2 10^ + ^2 80^ )+ ( ^2 15^ ^2 75^ )+ + ( ^2 40^ + ^2 50^ )+ ^2 45^ array & =(1)^2+ ( ^2 5^ + ^2 5^ )+ ( ^2 10^ + ^2 10^ ) & + ( ^2 15^ + ^2 15^ )+ + ( ^2 40^ + ^2 40^ )+ ( 1 2 )^2 & ^2 (90^ -5^ )= ^2 5^ and so on aligned gathered (II) ^2 5^ ^2 10^ ^2 15^ ^2 85^ = [ ( ^2 5^ ^2 85^ ) ( ^2 10^ ^2 80 ) . . ( ^2 40^ ^2 50^ ) ] ^2 45^ = [ ( ^2 5^ ^2 5^ ) ( ^2 10^ ^2 10^ ) . =[1.1 1] 1=1 gathered Hence (II) (D) aligned & (III) ^2 5^

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