Question

Simplify. $\sin (u-v) \cos v+\cos (u-v) \sin v$

   Simplify.
$\sin (u-v) \cos v+\cos (u-v) \sin v$

Algebra and Trigonometry

Algebra and Trigonometry

Beecher, Judith… 1st Edition

Chapter 7, Problem 76

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Solved by Expert Ankit Gupta

07/08/2020

Step 1

The sine addition formula states that \(\sin(a + b) = \sin a \cos b + \cos a \sin b\). Show more…

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Simplify. $\sin (u-v) \cos v+\cos (u-v) \sin v$

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Key Concepts

Trigonometric Identities

Trigonometric identities are essential relationships among sine, cosine, and other trigonometric functions that allow complex expressions to be transformed and simplified. They serve as a foundation for solving equations and proving other mathematical relationships.

Sine Addition Formula

The sine addition formula, which states that sin(a + b) = sin(a)cos(b) + cos(a)sin(b), is a key identity that enables the combination of sine and cosine terms into a single sine function. Recognizing this pattern facilitates the simplification of trigonometric expressions by converting them into a simpler form.

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