Trigonometry Identities - Product to Sum Identity True/False (Greek Letter)

Level 1

This math topic focuses on verifying trigonometric identities, specifically product-to-sum identities. It assesses the student's ability to determine whether each given identity is correct using True/False questions. The problems involve a variety of trigonometric expressions which combine sines and cosines with different angles, and students are required to judge the correctness of the resulting identities. Each question provides a visual representation in a LaTeX-rendered format, followed by options to answer 'Yes' or 'No,' making it clear and straightforward for the student to select the correct response based on their understanding of trigonometric transformations.

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

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

Trigonometry Identities - Product to Sum Identity True/False (Greek L...

Is this product to sum identity correct?

$A LaTex expression showing \text{sin}{(\gamma)}\text{cos}{(\alpha)} = 1 over 2 \left[ \text{cos}(\gamma + \alpha) + \text{sin}(\gamma + \alpha) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(\theta)}\text{cos}{(\beta)} = 1 over 2 \left[ \text{sin}(\theta + \beta) + \text{sin}(\theta - \beta) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(\beta)}\text{sin}{(\gamma)} = 1 over 2 \left[ \text{cos}(\beta + \gamma) + \text{cos} to the power of 2 (\beta + \gamma) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(\gamma)}\text{sin}{(\theta)} = 1 over 2 \left[ \text{cos}(\gamma + \theta) + \text{cos} to the power of 2 (\gamma + \theta) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(\beta)}\text{sin}{(\theta)} = 1 over 2 \left[ \text{sin}(\beta + \theta) + \text{sin}(\beta - \theta) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{sin}{(\theta)}\text{sin}{(\gamma)} = 1 over 2 \left[ \text{cos}(\theta - \gamma) - \text{cos}(\theta + \gamma) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(\alpha)}\text{cos}{(\gamma)} = 1 over 2 \left[ \text{cos}(\alpha + \gamma) + \text{cos} to the power of 2 (\alpha + \gamma) \right]$

Yes

Is this product to sum identity correct?

$A LaTex expression showing \text{cos}{(\alpha)}\text{cos}{(\beta)} = 1 over 2 \left[ \text{cos}(\alpha + \beta) + \text{cos} to the power of 2 (\alpha + \beta) \right]$

Yes