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AP EAMCET201922 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If ( 2 = cosec - ), then ( ^2 2 = )

Options

  1. A(2- 5 )
  2. B(-2+ 5 )
  3. C(2+ 5 )
  4. D( 2 +5 )

Correct answer

B. (-2+ 5 )

Step-by-step solution

Given, ( 2 = cosec - ) ( aligned & = 1 - = 1- ^2 & = ^2 = = (1- ^2 2 )^2 2 2 (1+ ^2 2 ) aligned ) ( aligned & 2 ^2 2 (1+ ^2 2 )=1+ ^4 2 -2 ^2 2 & 2 ^2 2 +2 ^4 2 =1+ ^4 2 -2 ^2 2 & ^4 2 +4 ^2 2 -1=0 & ^2 2 = -4 (4)^2-(-1) 4 2 1 = -4 16+4 2 & = -4 20 2 =-2 5 [ ^2 2 > 0 ] aligned )

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