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4 results for “sum to product”
Formulae (4)
Trigonometry
Advanced
Sum to Product: sin A + sin B
sin
A
+
sin
B
=
2
sin
A
+
B
2
cos
A
−
B
2
\sin A + \sin B = 2\sin\tfrac{A+B}{2}\cos\tfrac{A-B}{2}
sin
A
+
sin
B
=
2
sin
2
A
+
B
cos
2
A
−
B
Sum-to-product identity.
Trigonometry
Advanced
Sum to Product: sin A − sin B
sin
A
−
sin
B
=
2
cos
A
+
B
2
sin
A
−
B
2
\sin A - \sin B = 2\cos\tfrac{A+B}{2}\sin\tfrac{A-B}{2}
sin
A
−
sin
B
=
2
cos
2
A
+
B
sin
2
A
−
B
Sum-to-product identity.
Trigonometry
Advanced
Sum to Product: cos A + cos B
cos
A
+
cos
B
=
2
cos
A
+
B
2
cos
A
−
B
2
\cos A + \cos B = 2\cos\tfrac{A+B}{2}\cos\tfrac{A-B}{2}
cos
A
+
cos
B
=
2
cos
2
A
+
B
cos
2
A
−
B
Sum-to-product identity.
Trigonometry
Advanced
Sum to Product: cos A − cos B
cos
A
−
cos
B
=
−
2
sin
A
+
B
2
sin
A
−
B
2
\cos A - \cos B = -2\sin\tfrac{A+B}{2}\sin\tfrac{A-B}{2}
cos
A
−
cos
B
=
−
2
sin
2
A
+
B
sin
2
A
−
B
Sum-to-product identity.