Question

4 cos^2 п/8 - 4 sin^2 п/8​

Answer 1

Ответ:

корень из 2 делёное на 2))

Answer 2

Ответ:

Объяснение:

корень 2 деленное на 2

Answer 3

Let's simplify the expression:

4cos^2(π/8) - 4sin^2(π/8)

First, we can use the trigonometric identity:

cos(2θ) = cos^2(θ) - sin^2(θ)

So, in your expression, θ = π/8:

4cos^2(π/8) - 4sin^2(π/8) = 4cos^2(2(π/8)) - 4sin^2(2(π/8))

Now, apply the double angle formula for cosine:

cos(2θ) = 2cos^2(θ) - 1

So,

4cos^2(2(π/8)) - 4sin^2(2(π/8)) = 4(2cos^2(π/8) - 1) - 4sin^2(π/8)

Now, plug in the values:

4(2cos^2(π/8) - 1) - 4sin^2(π/8)

Now, calculate the values of cos(π/8) and sin(π/8):

cos(π/8) ≈ 0.9239 sin(π/8) ≈ 0.3827

Now, substitute these values into the expression:

4(2(0.9239^2) - 1) - 4(0.3827^2)

Calculate the squares and simplify:

4(2(0.8537) - 1) - 4(0.1463)

Now, perform the multiplications and subtractions:

4(1.7074 - 1) - 0.5852

Now, subtract and simplify:

6.8296 - 1.1704 ≈ 5.6592

So, the simplified value of the expression 4cos^2(π/8) - 4sin^2(π/8) is approximately 5.6592.