Cos^2A.sin^4A=1/32(2-2cos2A-2cos4A+cos6A)
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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
)
]
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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