Establish each identity. (sin(4 θ)+sin(8 θ))/(sin(4 θ)-sin(8 θ))=-(tan(6 θ))/(tan(2 θ))

Name: Problem 35, Chapter 7: Precalculus: pearson new international edition
Uploaded: 2020-06-19T04:28:11-08:00
Duration: 1 min 59 s
Channel: Amy Jiang
Description: Establish each identity. (sin(4 θ)+sin(8 θ))/(sin(4 θ)-sin(8 θ))=-(tan(6 θ))/(tan(2 θ))

step 1 So let's start with our left side. And I'll notice here in our numerator and our denominator, we

Establish each identity. (sin(4 θ)+sin(8 θ))/(sin(4 θ)-sin(8...

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Key Concepts

Verification of Trigonometric Identities

Verifying trigonometric identities involves using established trigonometric formulas, such as the sum-to-product relationships and the definition of tangent, to show that two expressions are equivalent. This process typically requires rewriting one or both sides of an equation using these identities and simplifying until a clear equivalence is established.

Sum-to-Product Identities

These identities convert sums or differences of trigonometric functions into products. For example, the identities sin A + sin B = 2 sin[(A+B)/2] cos[(A?B)/2] and sin A ? sin B = 2 cos[(A+B)/2] sin[(A?B)/2] are used to simplify expressions by reducing sums or differences to a product form, making further manipulation and comparison easier.

Tangent Function and Its Definition

The tangent function is defined as the ratio of sine to cosine for the same angle, tan ? = sin ? / cos ?. This definition allows one to transform expressions involving sine and cosine into expressions in terms of tangent. In verifying trigonometric identities, this transformation is useful in comparing and simplifying different forms of expressions.

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