Question

Sinx-cosx=-1 Решите пожалуйста

Answer 1

Sinx-cosx=-1
x=2πn,n∈Z или x=-π/2+2πn,n∈Z

Answer 2

Question

The question asks to solve the equation:

sinx - cosx = -1

Solution

To solve this equation, we can use trigonometric identities and rearrange terms:

`sinx - cosx = -1` `sinx + cosx = 1` (Adding 1 to both sides)

Using the identity `sin^2x + cos^2x = 1`:

`1 = sin^2x + cos^2x` `0 = (sinx + cosx)(sinx - cosx)` `0 = sinx + cosx` or `0 = sinx - cosx`

Therefore, the solutions are:

`sinx = 1, cosx = 0` `x = π/2 + kπ, k = 0, ±1, ±2, ...`

So the complete solution is:

x = π/2 + kπ, where k is any integer