Question

Express the product as sum or difference, 2 cos 32°. sin 18°​

Answer 1

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:

cosαcosβ+sinαsinβ=cos(α−β)

+cosαcosβ−sinαsinβ=cos(α+β)

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2cosαcosβ=cos(α−β)+cos(α+β)

Then, we divide by 2 to isolate the product of cosines:

cosαcosβ=

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.