Question

√2cos²π / 8-√2sin²π / 8 найдите значение выражения

Answer 1

Решение
√2cos²π / 8-√2sin²π / 8 = √2(cos²π / 8 - sin²π / 8) = √2 * cos(2 * π/8) =
= √2 * cos(π/4) = √2 * (√2/2) = 1

Answer 2

To find the value of the expression √2cos²(π/8) - √2sin²(π/8), we can use the trigonometric identity:

cos²θ - sin²θ = cos(2θ)

So, in this case, θ = π/8, and the expression becomes:

√2cos²(π/8) - √2sin²(π/8) = √2cos(2 * π/8)

Now, we can use the value of cos(π/4) to simplify further:

cos(π/4) = 1/√2

Substitute this value into the expression:

√2cos(2 * π/8) = √2 * cos(π/4) = √2 * (1/√2) = 1

Therefore, the value of the expression is 1.