Trigonometry Identities - Sum to Product to Identity (Greek Letter)

Level 1

This topic focuses on practicing trigonometric identities, specifically the transformation of sum-to-product identities. It includes a series of questions where the users must apply and manipulate trigonometric formulas involving sine and cosine functions of Greek letter variables such as \(\alpha\), \(\beta\), \(\gamma\), and \(\theta\). Each question presents an expression and requires the user to convert a sum of trigonometric functions into a product form, adhering to well-known identities. Multiple choice answers are provided for these problems, reinforcing the understanding of these identities and their application to simplify or restructure expressions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry Identities - Sum to Product to Identity (Greek Letter) Worksheet

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Trigonometry Identities - Sum to Product to Identity (Greek Letter)
1
Complete the sum to product identity for this expression
A LaTex expression showing \text{sin}{(\beta)}+\text{sin}{(\gamma)}
a A LaTex expression showing =\text{sin}{( 2 over (\beta + \gamma) )} \text{sin}{( (\beta - \gamma) over 2 )}
b A LaTex expression showing =2 \text{sin}{( (\beta + \gamma) over 2 )} \text{cos}{( (\beta - \gamma) over 2 )}
2
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(\alpha)}+\text{cos}{(\gamma)}
a A LaTex expression showing =2 \text{cos}{( (\alpha + \gamma) over 2 )} \text{cos}{( (\alpha - \gamma) over 2 )}
b A LaTex expression showing =2 \text{cos}{( 2 over (\alpha + \gamma) )} \text{cos}{( (\alpha - \gamma) over 2 )}
3
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(\gamma)}+\text{cos}{(\beta)}
a A LaTex expression showing =\text{cos}{( (\gamma + \beta) over 2 )} \text{cos}{( (\gamma + \beta) over 2 )}
b A LaTex expression showing =2 \text{cos}{( (\gamma + \beta) over 2 )} \text{cos}{( (\gamma - \beta) over 2 )}
4
Complete the sum to product identity for this expression
A LaTex expression showing \text{sin}{(\beta)}+\text{sin}{(\alpha)}
a A LaTex expression showing =\text{sin}{( 2 over (\beta + \alpha) )} \text{sin}{( (\beta - \alpha) over 2 )}
b A LaTex expression showing =2 \text{sin}{( (\beta + \alpha) over 2 )} \text{cos}{( (\beta - \alpha) over 2 )}
5
Complete the sum to product identity for this expression
A LaTex expression showing \text{sin}{(\alpha)}-\text{sin}{(\beta)}
a A LaTex expression showing =2 \text{cos}{( (\alpha + \beta) over 2 )} - \text{sin}{( (\alpha + \beta) over 2 )}
b A LaTex expression showing =2 \text{sin}{( (\alpha - \beta) over 2 )} \text{cos}{( (\alpha + \beta) over 2 )}
6
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(\alpha)}-\text{cos}{(\theta)}
a A LaTex expression showing =2 \text{sin}{( 2 over (\alpha + \theta) )} \text{cos}{( (\alpha - \theta) over 2 )}
b A LaTex expression showing =-2 \text{sin}{( (\alpha + \theta) over 2 )} \text{sin}{( (\alpha - \theta) over 2 )}
7
Complete the sum to product identity for this expression
A LaTex expression showing \text{cos}{(\beta)}+\text{cos}{(\gamma)}
a A LaTex expression showing =2 \text{sin}{( (\beta + \gamma) over 2 )} \text{sin}{( (\beta - \gamma) over 2 )}
b A LaTex expression showing =2 \text{cos}{( (\beta + \gamma) over 2 )} \text{cos}{( (\beta - \gamma) over 2 )}
8
Complete the sum to product identity for this expression
A LaTex expression showing \text{sin}{(\gamma)}+\text{sin}{(\theta)}
a A LaTex expression showing =2 \text{cos}{( (\gamma - \theta) over 2 )} - \text{sin}{( (\gamma + \theta) over 2 )}
b A LaTex expression showing =2 \text{sin}{( (\gamma + \theta) over 2 )} \text{cos}{( (\gamma - \theta) over 2 )}