simplify the expression:

sin(theta+pi/4) + sin(theta-pi/4)

To simplify the expression sin(theta + pi/4) + sin(theta - pi/4), we can use trigonometric identities to rewrite the sum of two sine functions as a single sine function.

First, let's use the sum identity for sine. According to the sum identity, sin(A + B) = sin(A)cos(B) + cos(A)sin(B).

Applying this identity to our expression, we have:
sin(theta + pi/4) + sin(theta - pi/4) = sin(theta)cos(pi/4) + cos(theta)sin(pi/4) + sin(theta)cos(-pi/4) - cos(theta)sin(-pi/4)

Now, we can simplify further. The cos(pi/4) and cos(-pi/4) both equal 1/sqrt(2) (or √2/2), and sin(pi/4) and sin(-pi/4) both equal 1/sqrt(2) (or √2/2).

Thus, the expression becomes:
sin(theta)*(√2/2) + cos(theta)*(√2/2) + sin(theta)*(√2/2) - cos(theta)*(√2/2)

Combining like terms, we get:
2 * sin(theta) * (√2/2) = √2 * sin(theta)

Therefore, the expression sin(theta + pi/4) + sin(theta - pi/4) simplifies to √2 * sin(theta).