Question

Sin x - cos x = 0 .............

Answer 1

Вот правильный ответ

Answer 2

To solve the equation sin(x) - cos(x) = 0, we'll need to find the values of x that satisfy this equation. We can use trigonometric identities to simplify the equation and then find the solutions.

Step 1: Apply the Pythagorean identity: sin^2(x) + cos^2(x) = 1 Step 2: Rearrange the original equation: sin(x) = cos(x) Step 3: Divide both sides by cos(x): tan(x) = 1 Step 4: Find the solutions for x:

The tangent function is equal to 1 at π/4 radians (45 degrees) in the first quadrant, and also at 5π/4 radians (225 degrees) in the third quadrant. However, since sin(x) = cos(x), the solutions repeat at π/4 + kπ and 5π/4 + kπ, where k is an integer (positive or negative).

So, the general solution for x is:

x = π/4 + kπ or x = 5π/4 + kπ, where k is an integer.

For example, some of the specific solutions for x are:

1. x = π/4 (45 degrees)
2. x = 5π/4 (225 degrees)
3. x = 5π/4 + π (315 degrees)
4. x = π/4 - π (225 degrees)

...and so on, with an increment of π (180 degrees) for each k.