How to solve $\sin(x) + 2\sqrt{2}\cos x =3$ How to solve $\sin(x) + 2\sqrt{2}\cos x=3$ ?
What is general method for doing these kind of questions?
Thanks

$$\sin  x+2\sqrt { 2 } \cos { x } =3\\ 2\sin { \frac { x }{ 2 } \cos { \frac { x }{ 2 } +2\sqrt { 2 } \left( \cos ^{ 2 }{ \frac { x }{ 2 } -\sin ^{ 2 }{ \frac { x }{ 2 }  }  }  \right) =3\sin ^{ 2 }{ \frac { x }{ 2 } +3\cos ^{ 2 }{ \frac { x }{ 2 }  }  }  }  } \\ \left( 3+2\sqrt { 2 }  \right) \sin ^{ 2 }{ \frac { x }{ 2 }  } -2\sin { \frac { x }{ 2 } \cos { \frac { x }{ 2 }  }  } +\left( 3-2\sqrt { 2 }  \right) \cos ^{ 2 }{ \frac { x }{ 2 }  } =0\\ \left( 3+2\sqrt { 2 }  \right) \tan ^{ 2 }{ \frac { x }{ 2 }  } -2\tan { \frac { x }{ 2 }  } +\left( 3-2\sqrt { 2 }  \right) =0\\ \tan { \frac { x }{ 2 } =\frac { 2\pm \sqrt { 3 }  }{ 2\left( 3+2\sqrt { 2 }  \right)  }  } \\ \\ \\ \\  $$
Can you take here?
