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Trigonometry Identities - Sum/Difference to Identity (Greek Letter)

Level 1

This topic focuses on practicing trigonometric identities, specifically transitioning sum and difference identities to standard identities using Greek letters as variable expressions. The math problems require completing expressions involving sine, cosine, and tangent of angles representing the sums or differences of two angles. Solutions are offered through multiple choice answers, requiring the identification of the correct trigonometric identity. This not only reinforces understanding of basic trigonometric identities but also helps in recognizing how they are applied and transformed in various mathematical contexts.

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

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Trigonometry Identities - Sum/Difference to Identity (Greek Letter) Worksheet

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