Practice Sum and Difference Identities in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Formulas that express \sin(A \pm B), \cos(A \pm B), and \tan(A \pm B) in terms of \sin A, \cos A, \sin B, and \cos B.
What happens when you combine two rotations? If you rotate by angle A and then by angle B, the result involves both angles interacting. The sum and difference formulas tell you exactly how the trig values of two separate angles combine. They're like a multiplication rule for rotations—the result isn't simply adding the trig values, but mixing sines and cosines together.
Example 1
easyFind the exact value of \cos(75°) using the sum identity.
Example 2
mediumSimplify \sin(x + y) + \sin(x - y).
Example 3
mediumFind the exact value of \tan(15°) using a difference identity.
Example 4
hardIf \sin(\alpha) = \frac{4}{5} with \alpha in QI and \cos(\beta) = -\frac{5}{13} with \beta in QII, find \cos(\alpha + \beta).