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Trigonometry Identities - Power Reducing to Identity (Greek Letter)

Level 1

This math topic focuses on practicing trigonometric identities, specifically power reducing identities involving the square powers of sine, cosine, and tangent functions. Students are required to complete the identities for given trigonometric expressions. Each problem presents a trigonometric expression squared, like cos²(θ) or sin²(α), and students need to select the correct identity transformation from options provided. This topic is designed to enhance understanding of how to manipulate and simplify expressions using fundamental trigonometric identities.

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

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Trigonometry Identities - Power Reducing to Identity (Greek Letter) Worksheet

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