Trigonometrisk Ekvation - Fortsättning

t = x + {%pi} over {3}newline 2cos^2(t) - {sqrt{3} } over {2} sin2(t) + 3sin^2(t) = 2 newline (2cos^2(t)+2sin^2(t))+sin^2(t)-{sqrt{3} } over {2} sin2(t)=2 newline 2 + sin^2(t)-{sqrt{3} } over {2} sin2(t)=2 newline sin^2(t)-{sqrt{3} } over {2} sin2(t)=0 newline sin^2(t)-{sqrt{3} } over {2}2sin(t)cos(t)=0 newline sin^2(t)-sqrt{3}sin(t)cos(t)=0 newline sin(t)(sin(t)-sqrt{3}cos(t))=0 newline newline sin(t)=0 newline sin(t)-sqrt{3} cos(t)=0 newline newline x_{1}=-{%pi} over {3}~~~~x_{2}={2%pi} over {3}

t = x + {%pi} over {3}newline 2cos^2(t) - {sqrt{3} } over {2} sin2(t) + 3sin^2(t) = 2 newline (2cos^2(t)+2sin^2(t))+sin^2(t)-{sqrt{3} } over {2} sin2(t)=2 newline 2 + sin^2(t)-{sqrt{3} } over {2} sin2(t)=2 newline sin^2(t)-{sqrt{3} } over {2} sin2(t)=0 newline sin^2(t)-{sqrt{3} } over {2}2sin(t)cos(t)=0 newline sin^2(t)-sqrt{3}sin(t)cos(t)=0 newline sin(t)(sin(t)-sqrt{3}cos(t))=0 newline newline sin(t)=0 newline sin(t)-sqrt{3} cos(t)=0 newline newline x_{1}=-{%pi} over {3}~~~~x_{2}={2%pi} over {3} newline newline tan(t)=sqrt{3} newline t={%pi} over {3} ~ rightarrow ~ x_{3} = 0 newline newline SVAR: newline newline x_{1} = -{%pi} over {3}+n*2%pi ~~~x_{2}={2%pi} over {3} +n*2%pi ~~~x_{3} = 0 + 2%pi