Trigonometry Rules

Sine rule:

\frac { a }{ sinA } =\frac { b }{ sinB } =\frac { c }{ sinC }

Other:

sin\left( -\theta \right) =-sin\theta \\ \\ cos\left( -\theta \right) =cos\theta \\ \\ tan\left( -\theta \right)= -tan\theta

Important identities:

{ sin }^{ 2 }\theta +{ cos }^{ 2 }\theta =1

1+\tan ^{ 2 }{ \theta  } =\sec ^{ 2 }{ \theta  } 

1+\cot ^{ 2 }{ \theta  } =\csc ^{ 2 }{ \theta  } 

Trigonometric fractions:

\sec ^{ 2 }{ \theta  } =\frac { 1 }{ \cos ^{ 2 }{ \theta  }  } ,\quad \therefore \quad \cos ^{ 2 }{ \theta  } =\frac { 1 }{ \sec ^{ 2 }{ \theta  }  } \\ \\ \csc ^{ 2 }{ \theta  } =\frac { 1 }{ \sin ^{ 2 }{ \theta  }  } ,\quad \therefore \quad \sin ^{ 2 }{ \theta  } =\frac { 1 }{ \csc ^{ 2 }{ \theta  }  } \\ \\ \cot ^{ 2 }{ \theta  } =\frac { 1 }{ \tan ^{ 2 }{ \theta  }  } ,\quad \therefore \quad \tan ^{ 2 }{ \theta  } =\frac { 1 }{ \cot ^{ 2 }{ \theta  }  } 

Area of a triangle:

\frac { 1 }{ 2 } bcsinA=\frac { 1 }{ 2 } acsinB=\frac { 1 }{ 2 } absinC

Pythagoras’s Theorem:

{ a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }

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