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Trigonometry Identities - Double Angle to Identity (Greek Letter)

Level 1

This topic focuses on practicing trigonometric double-angle identities. It presents problems that require completing expressions for double-angle formulas involving the trigonometric functions sine, cosine, and tangent. Each question provides two potential solutions, and the students must identify or confirm the correct trigonometric identity corresponding to the given expressions using Greek letter variables like alpha, gamma, and theta. This exercise is suitable for reinforcing understanding of trigonometric identities in a beginner-level context within a broader unit on introductory trigonometric identities.

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

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Trigonometry Identities - Double Angle to Identity (Greek Letter) Worksheet

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Trigonometry Identities - Double Angle to Identity (Greek Letter)
1
A LaTex expression showing \text{cos}{(2 times \gamma)}
Complete the double-angle identity for this expression
a A LaTex expression showing =2\text{cos} to the power of 2 (\gamma) - 1
b A LaTex expression showing =1 + 2\text{sin} to the power of 2 (\gamma)
2
A LaTex expression showing \text{tan}{(2 times \alpha)}
Complete the double-angle identity for this expression
a A LaTex expression showing =\frac{2\text{tan}(\alpha)}{1-\text{tan} to the power of 2 (\alpha)}
b A LaTex expression showing =\frac{\text{tan}(\alpha)}{1-2\text{tan}(\alpha)}
3
A LaTex expression showing \text{sin}{(2 times \gamma)}
Complete the double-angle identity for this expression
a A LaTex expression showing =2\text{sin}(\gamma)\text{cos}(\gamma)
b A LaTex expression showing =\frac{\text{sin}(\gamma)\text{cos}(\gamma)}{2}
4
A LaTex expression showing \text{tan}{(2 times \theta)}
Complete the double-angle identity for this expression
a A LaTex expression showing =\frac{2\text{tan}(\theta)}{1-\text{tan} to the power of 2 (\theta)}
b A LaTex expression showing =\frac{\text{tan}(\theta)}{1-2\text{tan}(\theta)}
5
Complete the double-angle identity for this expression
A LaTex expression showing \text{cos}{(2 times \alpha)}
a A LaTex expression showing =\text{cos} to the power of 2 (\alpha) - \text{sin} to the power of 2 (\alpha)
b A LaTex expression showing =2\text{cos} to the power of 2 (\alpha) + 1
6
A LaTex expression showing \text{cos}{(2 times \theta)}
Complete the double-angle identity for this expression
a A LaTex expression showing =2\text{cos} to the power of 2 (\theta) + 1
b A LaTex expression showing =2\text{cos} to the power of 2 (\theta) - 1
7
A LaTex expression showing \text{sin}{(2 times \theta)}
Complete the double-angle identity for this expression
a A LaTex expression showing =\frac{2\text{tan}(\theta)}{1+\text{tan} to the power of 2 (\theta)}
b A LaTex expression showing =\frac{\text{sin}(\theta)\text{cos}(\theta)}{2}
8
A LaTex expression showing \text{sin}{(2 times \alpha)}
Complete the double-angle identity for this expression
a A LaTex expression showing =\text{sin}(\alpha)\text{cos}(\alpha)
b A LaTex expression showing =2\text{sin}(\alpha)\text{cos}(\alpha)