The expression you provided is:

\[
\sin(a) + \cos(a)
\]

This cannot be simplified further without additional context, such as specific values for \( a \) or additional trigonometric identities.

However, if you wanted to write it in an alternative form, one option is to use the trigonometric identity for a sum of sines and cosines. The general form for combining \(\sin(a)\) and \(\cos(a)\) into a single sine term is:

\[
\sin(a) + \cos(a) = \sqrt{2} \sin\left(a + \frac{\pi}{4}\right)
\]

This identity allows you to express the sum of sine and cosine as a single sine function with an amplitude of \( \sqrt{2} \) and a phase shift of \( \frac{\pi}{4} \).

Would you like more details or have any specific questions?

Here are 5 related questions:
1. What is the value of \( \sin(a) + \cos(a) \) when \( a = \frac{\pi}{4} \)?
2. How can we derive the identity \( \sin(a) + \cos(a) = \sqrt{2} \sin\left(a + \frac{\pi}{4}\right) \)?
3. What is the graph of \( \sin(a) + \cos(a) \) over one period?
4. How can we express \( \sin(a) + \cos(a) \) using Euler's formula?
5. What happens if you square both sides of \( \sin(a) + \cos(a) \)?

**Tip:** When adding trigonometric functions, combining them into a single sine or cosine term can simplify solving equations or graphing.

Understand how to simplify the expression sin(a) + cos(a) using trigonometric identities. Learn how to combine sine and cosine into a single sine function with an amplitude of √2 and a phase shift of π/4. Suitable for students in Grades 10-12.

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