Question

Решить уравнение: sin x - cos x = 0

Answer 1

I hope this helps you

Answer 2

To solve the equation sin(x) - cos(x) = 0, we need to find the values of x that satisfy this equation. First, we'll manipulate the equation to express one trigonometric function in terms of the other:

sin(x) - cos(x) = 0

Adding cos(x) to both sides:

sin(x) = cos(x)

Next, we can use the trigonometric identity tan(x) = sin(x)/cos(x) to simplify further:

tan(x) = 1

Now, we need to find the values of x for which the tangent of x is equal to 1. To do that, we can recall the common values of the tangent function. The tangent function has a value of 1 at π/4 radians (45 degrees) and also at any odd multiple of π/4 radians. So, the solutions for x are:

x = π/4 + nπ (where n is an integer)

This represents the general solution to the equation sin(x) - cos(x) = 0. The solution is a set of all angles that are π/4 radians (45 degrees) more than any odd multiple of π radians.