Solve the following equation, and state all real solutions in radians3 sin(2x) - cos^2(2x) - 1 = 0 

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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`3sin(2x) - cos^2 (2x) -1 = 0`

`3sin(2x) - (1-sin^2 (2x)) -1 = 0`

`3sin(2x) -1 +sin^2 (2x) -1 = 0`

`sin^2 (2x) + 3sin(2x) -2 = 0`

`==> sin(2x) = (-3 +sqrt(9+8))/2 = (-3+sqrt17)/2 =0.5616 `

`==> 2x = 34.17 `

`==> x = 17.09`

`==> sin(2x) = (-3-sqrt17)/2 = -3.56`

`==> x = 17.09^(o)`

 

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