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The value of \(\sin(x + y)\) is approximately \(0.969\).

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Here are five more questions you might want to ask:

1. How do I find the value of \(\tan(\alpha \tan \theta)\)?
2. Can you explain how to reduce the expression in problem 2?
3. How do you calculate \(K = \tan(x + y)\) given \(\sin(x) = \frac{1}{\sqrt{5}}\) and \(\cos(y) = \frac{2}{3}\)?
4. How can I find \(\tan \alpha\) using the given triangle?
5. How do I reduce \(\sqrt{2} \cos(45^\circ + x) - \cos x\)?

**Tip:** When working with trigonometric identities, it's helpful to remember the fundamental identities and angle addition formulas to simplify expressions effectively.

Discover how to solve for \(\sin(x + y)\) using the angle addition formula. This page provides a detailed solution, including key trigonometric identities and related questions to deepen your understanding. Ideal for high school students (Grades 10-12) studying trigonometry.

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