9 + √2 * sin^2 альфа - √2 * соs^2 альфа (альфа = Pi/8)

Предыдущий
вопрос Следующий
вопрос

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