use the formula and write in product from.
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We can derive the product-to-sum formula from the sum and difference identities for cosine. If we add the two equations, we get:
cos
α
cos
β
+
sin
α
sin
β
=
cos
(
α
−
β
)
+
cos
α
cos
β
−
sin
α
sin
β
=
cos
(
α
+
β
)
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
2
cos
α
cos
β
=
cos
(
α
−
β
)
+
cos
(
α
+
β
)
Then, we divide by \displaystyle 22 to isolate the product of cosines:
cos
α
cos
β
=
1
2
[
cos
(
α
−
β
)
+
cos
(
α
+
β
)
]
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