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More Trigonometric Identities
Formulae
Multiple Angles and Functions
Formulae
Double and Half-Angle Formulas
Problems
Addition and Subtraction Formulas
Problems
Products of Functions
Problems
Sums and Differences of Functions
Problems
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Multiple Angles and Functions
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Double and Half-Angle Formulas
More Trigonometric Identities
Formulae
Addition of Angles
sin(
α
+
β
) = sin(
α
)cos(
β
) + cos(
α
)sin(
β
);
cos(
α
+
β
) = cos(
α
)cos(
β
) - sin(
α
)sin(
β
);
tan(
α
+
β
) =
Double Angle
sin(2
x
) = 2 sin(
x
)cos(
x
);
cos(2
x
) = cos
2
(
x
) - sin
2
(
x
) = 1 - 2 sin
2
(
x
) = 2 cos
2
(
x
) - 1;
tan(2
x
) =
Function Products
sin(
α
)sin(
β
) = -
(cos(
α
+
β
) - cos(
α
-
β
));
cos(
α
)cos(
β
) =
(cos(
α
+
β
) + cos(
α
-
β
));
sin(
α
)cos(
β
) =
(sin(
α
+
β
) + sin(
α
-
β
));
cos(
α
)sin(
β
) =
(sin(
α
+
β
) - sin(
α
-
β
))
Function Sums and Differences
sin(
α
) + sin(
β
) = 2 sin
cos
;
cos(
α
) + cos(
β
) = 2 cos
cos
;
sin(
α
) - sin(
β
) = 2 cos
sin
;
cos(
α
) - cos(
β
) = - 2 sin
sin
Half Angle
sin(
) = ±
;
cos(
) = ±
;
tan(
) = ±
=
=
Subtraction of Angles
sin(
α
-
β
) = sin(
α
)cos(
β
) - cos(
α
)sin(
β
);
cos(
α
-
β
) = cos(
α
)cos(
β
) + sin(
α
)sin(
β
);
tan(
α
-
β
) =
.
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(cos(α + β) - cos(α - β));
cos
;
) = ±
;
;
= 
= 
