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

Level 1

This math topic focuses on practicing trigonometric identities, specifically transforming products of sine and cosine functions into sum and difference identities. Users solve problems where they must apply product-to-sum identities to different trigonometric expressions involving variables represented by Greek letters such as α (alpha), β (beta), γ (gamma), and θ (theta). Each problem provides a trigonometric expression and asks the user to complete it correctly using these identities. The solutions use various combinations of sine and cosine functions with added or subtracted arguments.

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

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

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