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AP EAMCET202419 May 2024Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The smallest positive value (in degrees) of for which ( +100^ )= ( +50^ ) ( ) ( -50^ ) is valid, is

Options

  1. A60^
  2. B45^
  3. C30^
  4. D15^

Correct answer

C. 30^

Step-by-step solution

Given, ( +100^ )= ( +50^ ) ( -50^ ) ( +100^ ) ( -50^ ) = ( +50^ ) aligned & ( +100^ ) ( -50^ ) ( +100^ ) ( -50^ ) = ( +50^ ) ( +50^ ) & ( +100^ ) ( -50^ )+ ( +100^ ) ( -50^ ) ( +100^ ) ( -50^ )- ( +100^ ) ( -50^ ) & = ( +50^ ) + ( +50^ ) ( +50^ ) - ( +50^ ) & (2 +50^ ) (150^ ) = (50^ ) - (2 +50^ ) & (2 +50^ ) (2 +50^ )+ (50^ ) (150^ )=0 & (4 +100^ )+ 50^ =0 & (4 +100^ )=- (50^ )= (220^ ) & 4 +100^ =220^ 4 =120^ aligned =30^ . (It is smallest positive value)

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