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

Level 1

This topic focuses on testing understanding of trigonometric sum-to-product identities. The problems involve deciding whether given sum-to-product formulas are correct using true/false questions. They use degrees for angular measurements and the problems feature a variety of trigonometric functions — sine and cosine. Students are shown trigonometric expressions and must decide whether they are valid representations of the sum-to-product 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 (Degrees) Worksheet

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Trigonometry Identities - Sum to Product Identity True/False (Degrees)
1
Is this sum to product identity correct?
A LaTex expression showing \text{cos}{(300 to the power of circle )}-\text{cos}{(210 to the power of circle )} = 2 \text{sin}{( 2 over (300 to the power of circle + 210^{ circle )})} \text{cos}{( \frac{(300 to the power of circle - 210 to the power of circle )}{2})}
a
Yes
b
No
2
Is this sum to product identity correct?
A LaTex expression showing \text{cos}{(30 to the power of circle )}+\text{cos}{(150 to the power of circle )} = \text{cos}{( \frac{(30 to the power of circle + 150 to the power of circle )}{2})} \text{cos}{( \frac{(30 to the power of circle + 150 to the power of circle )}{2})}
a
Yes
b
No
3
Is this sum to product identity correct?
A LaTex expression showing \text{sin}{(120 to the power of circle )}+\text{sin}{(300 to the power of circle )} = \text{sin}{( 2 over (120 to the power of circle + 300^{ circle )})} \text{sin}{( \frac{(120 to the power of circle - 300 to the power of circle )}{2})}
a
Yes
b
No
4
Is this sum to product identity correct?
A LaTex expression showing \text{cos}{(135 to the power of circle )}+\text{cos}{(300 to the power of circle )} = 2 \text{cos}{( \frac{(135 to the power of circle + 300 to the power of circle )}{2})} \text{cos}{( \frac{(135 to the power of circle - 300 to the power of circle )}{2})}
a
Yes
b
No
5
Is this sum to product identity correct?
A LaTex expression showing \text{cos}{(300 to the power of circle )}-\text{cos}{(225 to the power of circle )} = -2 \text{sin}{( \frac{(300 to the power of circle + 225 to the power of circle )}{2})} \text{sin}{( \frac{(300 to the power of circle - 225 to the power of circle )}{2})}
a
Yes
b
No
6
Is this sum to product identity correct?
A LaTex expression showing \text{sin}{(210 to the power of circle )}+\text{sin}{(300 to the power of circle )} = 2 \text{sin}{( \frac{(210 to the power of circle + 300 to the power of circle )}{2})} \text{cos}{( \frac{(210 to the power of circle - 300 to the power of circle )}{2})}
a
Yes
b
No
7
Is this sum to product identity correct?
A LaTex expression showing \text{sin}{(45 to the power of circle )}+\text{sin}{(300 to the power of circle )} = \text{sin}{( 2 over (45 to the power of circle + 300^{ circle )})} \text{sin}{( \frac{(45 to the power of circle - 300 to the power of circle )}{2})}
a
Yes
b
No
8
Is this sum to product identity correct?
A LaTex expression showing \text{cos}{(30 to the power of circle )}-\text{cos}{(315 to the power of circle )} = -2 \text{sin}{( \frac{(30 to the power of circle + 315 to the power of circle )}{2})} \text{sin}{( \frac{(30 to the power of circle - 315 to the power of circle )}{2})}
a
Yes
b
No