Question

(sin^2 45+cos^2 45)^2 + (sin^2 45-cos^2 45)^2 =

Answer 1

=1²-соs90°=1

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Answer 2

Let's calculate the given expression step by step:

We know that sin(45 degrees) = cos(45 degrees) = 1/sqrt(2).

1. (sin^2 45 + cos^2 45)^2: (1/sqrt(2))^2 + (1/sqrt(2))^2 = (1/2 + 1/2)^2 = (1)^2 = 1

2. (sin^2 45 - cos^2 45)^2: (1/sqrt(2))^2 - (1/sqrt(2))^2 = (1/2 - 1/2)^2 = (0)^2 = 0

Now, we add both results:

1 + 0 = 1

So, (sin^2 45 + cos^2 45)^2 + (sin^2 45 - cos^2 45)^2 = 1.