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2sin² A = 4 + 3cos A
=> sin² A + cos² A = 1
=> sin² A = ( 1 - cos² A )
=> 2 ( 1 - cos² A ) = 4 + 3 cos A
=> 2 - 2cos² A = 4 + 3 cos A
=> 2 cos² A + 3 cos A + 2 = 0
Discriminant of the above equation is ,
=> √ { (3)² - 4 (2)(2) }
=> √ { 9 -16 }
=> √ -7 = √7 i
so , the above equation has NO REAL ROOTS .
Therefore , there are 0 values of A in the interval [ 0 , 2π ] .
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