Question

Sin 2 x-2sinx cos x = 8 cos 2 x​

Answer 1

Ответ:фото смотри

Объяснение: в однородном уравнении можно БЕЗ ДОКАЗАТЕЛЬСТВА ТОГО, ЧТО cos^2(x) ≠ 0 делить на косинус в квадрате

Answer 2

To solve the trigonometric equation sin(2x) - 2sin(x)cos(x) = 8cos(2x), you can use trigonometric identities to simplify and solve it step by step. Here's how to do it:

1. Start by using the double angle formula for sine: sin(2x) = 2sin(x)cos(x).

The equation becomes: 2sin(x)cos(x) - 2sin(x)cos(x) = 8cos(2x).

Now, the equation simplifies to: 0 = 8cos(2x).

2. Divide both sides of the equation by 8: 0 = cos(2x).

3. Now, solve for x by finding the angles where cos(2x) equals zero. Recall that the cosine function is zero at odd multiples of π/2.

So, we have: 2x = π/2 + nπ, where n is an integer.

Now, divide both sides by 2: x = (π/2 + nπ)/2.

This gives you the general solution for x: x = π/4 + (nπ)/2, where n is an integer.

So, the solution to the equation sin(2x) - 2sin(x)cos(x) = 8cos(2x) is: x = π/4 + (nπ)/2, where n is an integer.