Verified answer

1) cos^2(-π/4) + cos^2(-π/4)

2) 2 * cos^2(-π/4)

3) 2 * cos(-π/4) * cos(-π/4)

4) 2 * cos(π/4) * cos(π/4)

5) 2 * [(sqrt2)/2] * [(sqrt2)/2]

6) 2 * (2/4)

7) 2 * (1/2)

8) 1

From the first step to the second, "cos^2(-π/4) + cos^2(-π/4)" is the same as "2 times cos^2(-π/4)," and then "cos^2(-π/4)" is the same as cos(-π/4) * cos(-π/4). A property of the cosine function is that if you plug something in that's negative (like -π/4), it will be equal to if you plugged in the positive form of the number, so cos(-π/4) = cos(π/4). Then, cos(π/4) equals the square root of 2 divided by 2. If you squared that, the product would be 2/4 which reduces to 1/2. Finally, you multiply it by 2 and the answer is 1.

Yeah, you probably didn't need that much info. Lol. Anyway, hope it wasn't confusing.