Question

Sin2x*cos2x=1/4 Первоначально очень подробно. как что получилось

Answer 1

РЕШЕНИЕ СМОТРИ НА ФОТОГРАФИИ

Answer 2

Solving the Equation sin(2x) * cos(2x) = 1/4

To solve the equation sin(2x) * cos(2x) = 1/4, we can use trigonometric identities and algebraic manipulation. Let's break down the steps:

Step 1: Use the double-angle identity for sine and cosine: - sin(2x) = 2 * sin(x) * cos(x) - cos(2x) = cos^2(x) - sin^2(x)

Step 2: Substitute the double-angle identities into the equation: - 2 * sin(x) * cos(x) * (cos^2(x) - sin^2(x)) = 1/4

Step 3: Simplify the equation: - 2 * sin(x) * cos(x) * cos^2(x) - 2 * sin(x) * cos(x) * sin^2(x) = 1/4

Step 4: Expand and rearrange the terms: - 2 * sin(x) * cos(x) * cos^2(x) - 2 * sin(x) * cos(x) * sin^2(x) = 1/4 - 2 * sin(x) * cos(x) * (cos^2(x) - sin^2(x)) = 1/4 - 2 * sin(x) * cos(x) * (cos^2(x) - (1 - cos^2(x))) = 1/4 - 2 * sin(x) * cos(x) * (2 * cos^2(x) - 1) = 1/4

Step 5: Simplify further: - 4 * sin(x) * cos(x) * (2 * cos^2(x) - 1) = 1

At this point, we have simplified the equation, but it is not possible to solve it algebraically. We can use numerical methods or graphing to find approximate solutions.

Please note that the equation sin(2x) * cos(2x) = 1/4 is a transcendental equation, which means it cannot be solved exactly using algebraic methods. Numerical methods or approximations are typically used to find solutions.

I hope this explanation helps! Let me know if you have any further questions.