To simplify this expression, we first need to calculate the value of sin^2(𝛼) and cos^2(𝛼) when 𝛼 = π/8.
Given 𝛼 = π/8, we have:
sin(𝛼) = sin(π/8) ≈ 0.383cos(𝛼) = cos(π/8) ≈ 0.924
Now, let's substitute these values into the expression:
9 + √2 (0.383)^2 - √2 (0.924)^29 + √2 0.146929 - √2 0.8537769 + 0.344953√2 - 1.204507√29 - 0.859554√2
Therefore, the simplified expression is:
9 - 0.859554√2
To simplify this expression, we first need to calculate the value of sin^2(𝛼) and cos^2(𝛼) when 𝛼 = π/8.
Given 𝛼 = π/8, we have:
sin(𝛼) = sin(π/8) ≈ 0.383
cos(𝛼) = cos(π/8) ≈ 0.924
Now, let's substitute these values into the expression:
9 + √2 (0.383)^2 - √2 (0.924)^2
9 + √2 0.146929 - √2 0.853776
9 + 0.344953√2 - 1.204507√2
9 - 0.859554√2
Therefore, the simplified expression is:
9 - 0.859554√2