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

Level 1

This topic focuses on verifying the correctness of trigonometric identities, specifically sum to product identities. Each problem presents a trigonometric identity formula involving sine or cosine functions with variables represented by Greek letters. Students are required to determine whether these identities are true or false and select the appropriate answer. This involves understanding and applying the formulas for transforming sums into products within trigonometry. The content aims to bolster students' comprehension and skills in manipulating and verifying trigonometric identities.

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

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

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

Is this sum to product identity correct?

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

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(\beta)}+\text{sin}{(\alpha)} = \text{sin}{( 2 over (\beta + \alpha) )} \text{sin}{( (\beta - \alpha) over 2 )}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{cos}{(\gamma)}-\text{cos}{(\beta)} = -2 \text{sin}{( (\gamma + \beta) over 2 )} \text{sin}{( (\gamma - \beta) over 2 )}$

Yes

Is this sum to product identity correct?

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

Yes

Is this sum to product identity correct?

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

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{cos}{(\alpha)}-\text{cos}{(\beta)} = 2 \text{sin}{( 2 over (\alpha + \beta) )} \text{cos}{( (\alpha - \beta) over 2 )}$

Yes

Is this sum to product identity correct?

$A LaTex expression showing \text{sin}{(\beta)}+\text{sin}{(\gamma)} = \text{sin}{( 2 over (\beta + \gamma) )} \text{sin}{( (\beta - \gamma) over 2 )}$

Yes

Is this sum to product identity correct?

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

Yes