Math / Trigonometry

QuestionFill in the blank to complete the trigonometric formula. $\sin u \cos v=$

Studdy Solution

STEP 1

1. The problem requires knowledge of trigonometric identities.
2. We are looking for a known trigonometric identity that involves $\sin u$ and $\cos v$ .

STEP 2

1. Identify the relevant trigonometric identity.
2. Write the complete identity.

STEP 3

Identify the relevant trigonometric identity. The product-to-sum identities are useful here. The identity for $\sin u \cos v$ is:
$\sin u \cos v = \frac{1}{2} [\sin(u+v) + \sin(u-v)]$

STEP 4

Write the complete identity in the blank:
$\sin u \cos v = \frac{1}{2} [\sin(u+v) + \sin(u-v)]$
This completes the trigonometric formula.

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