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AP EAMCET201920 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

( ^2 5^ - ^2 15^ - ^2 15^ + ^2 35^ ) (+ 15^ 15^ - 5^ 35^ = )

Options

  1. A0
  2. B1
  3. C( 3 2 )
  4. D2

Correct answer

A. 0

Step-by-step solution

( aligned & ^2 5^ - ^2 15^ - ^2 15^ + ^2 35^ & + 15^ 15^ - 5^ 35^ & = 5^ ( 5^ - 35^ )- 15^ ( 15^ - 15^ ) & + ^2 35^ - ^2 15^ & = 5^ ( 5^ - 55^ )- 15^ ( 15^ - 75^ ) & + 50^ 20^ & = 5^ (2 30^ 25^ )- 15^ (2 45^ 30^ ) & + 50^ 20^ & =- 15^ 2 + 5^ 25^ + 50^ 20^ & =- 15^ 2 + 1 2 (2 5^ 65^ )+ 1 2 (2 50^ 20^ ) & =- 15^ 2 + 1 2 [ 70^ + 60^ + 30^ - 70^ ] & =- 15^ 2 + 1 2 [2 45^ 15^ ] & =- 15^ 2 + 15^ 2 =0 aligned ) Hence, option (1) is correct.

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