Express the product as a sum ordifference, 2 cos 34. cos 2A=...
Answers
Answer:
Expressing Products as Sums for Cosine
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
)
]
Step-by-step explanation:
Expressing Products as Sums
We have already learned a number of formulas useful for expanding or simplifying trigonometric expressions, but sometimes we may need to express the product of cosine and sine as a sum. We can use the product-to-sum formulas, which express products of trigonometric functions as sums. Let’s investigate the cosine identity first and then the sine identity.