Question

Плиз sin²2x-cos²2x=\/3/2

Answer 1

Ответ:

x = ±5π/24 + 0.5π*n (n∈Z)

Пошаговое объяснение:

sin²2x - cos²2x = √3/2

cos²2x - sin²2x = -√3/2

cos(4x) = -√3/2 (по формуле cos(2a) = cos²(a) - sin²(a))

4x = ±5π/6 + 2π*n (n∈Z)

x = ±5π/24 + 0.5π*n (n∈Z)

Answer 2

The equation you've provided is a trigonometric equation involving sine and cosine functions. It's written as:

sin²(2x) - cos²(2x) = √(3)/2

To solve this equation, we can use trigonometric identities to simplify the left side of the equation. One of the fundamental trigonometric identities is the Pythagorean identity, which states that sin²θ + cos²θ = 1. Using this identity, we can rewrite the equation as:

1 - 2cos²(2x) = √(3)/2

Now, we'll isolate the cosine term by subtracting 1 from both sides:

-2cos²(2x) = √(3)/2 - 1

Divide both sides by -2:

cos²(2x) = (1 - √(3)/2)

Now, take the square root of both sides:

cos(2x) = ±√(1 - √(3)/2)

cos(2x) = ±√(2 - √3)/2

Now, to find the possible values of x, we need to consider the range of the cosine function, which is -1 to 1. The values of cos(2x) can only be between -1 and 1. Since ±√(2 - √3)/2 is greater than 1, there are no real solutions for this equation.

In summary, the original equation sin²(2x) - cos²(2x) = √(3)/2 has no real solutions for x that satisfy the equation.