Question

Sinx+cos(2П+x)-cos(П/2-x)=-1

Answer 1

Sinx+cosx-sinx=-1
cosx=-1
x=π+2πn

Answer 2

To solve the equation sin(x) + cos(2π + x) - cos(π/2 - x) = -1, we can simplify the trigonometric expressions and then solve for x.

First, let's simplify the equation step by step:

sin(x) + cos(2π + x) - cos(π/2 - x) = -1

Using the properties of cosine and sine functions:

sin(x) + cos(2π)cos(x) - sin(2π)sin(x) - cos(π/2)cos(x) + sin(π/2)sin(x) = -1

Simplifying further:

sin(x) + cos(x) - cos(x) - sin(x) = -1

The terms involving 2π cancel out since cos(2π) = 1 and sin(2π) = 0. Similarly, cos(π/2) = 0 and sin(π/2) = 1.

Simplifying even more:

0 = -1

Since the equation simplifies to 0 = -1, we can see that there is no solution that satisfies the equation.