2cos квадрат 3x+sin5x=1

Предыдущий
вопрос Следующий
вопрос

The given equation is:

2cos^2(3x) + sin(5x) = 1

Using the trigonometric identity cos^2(x) + sin^2(x) = 1, we can rewrite the equation as:

2(1 - sin^2(3x)) + sin(5x) =
2 - 2sin^2(3x) + sin(5x) = 1

Let's rewrite sin(5x) using the double angle formula for sine:

sin(5x) = 2sin(2x)cos(3x)

Substitute it back into the equation:

2 - 2sin^2(3x) + 2sin(2x)cos(3x) =
2sin(2x)cos(3x) - 2sin^2(3x) = -
2sin(2x)cos(3x) - 2(1 - cos^2(3x)) = -1

Expand:

2sin(2x)cos(3x) - 2 + 2cos^2(3x) = -
2sin(2x)cos(3x) + 2cos^2(3x) = 1

This equation cannot be simplified further without additional information or context.