α is an acute angle.(sin α + cos α)

It seems like you didn't provide a specific question. However, if you're asking for the maximum value of the expression "sin α + cos α" where α is an acute angle, here are the steps:

1. We know that sin^2 α + cos^2 α = 1 for all α. This is the Pythagorean identity.

2. If we want to maximize the expression sin α + cos α, we can square it and then take the square root at the end (since the square root function is increasing).

3. (sin α + cos α)^2 = sin^2 α + cos^2 α + 2sin α cos α = 1 + 2sin α cos α.

4. We know that 2sin α cos α is the double angle formula for sin(2α). The maximum value of sin(2α) is 1.

5. Therefore, the maximum value of 1 + 2sin α cos α is 1 + 1 = 2.

6. Taking the square root, the maximum value of sin α + cos α is sqrt(2).

So, the maximum value of sin α + cos α for an acute angle α is sqrt(2).