check if this works sinx+cosx=0
sinx=-cosx
now deivde them by postive cosx
get tanx=-1
and if this wordk how does it work
Yes, this works.
To understand how it works, let's first rewrite the equation sinx + cosx = 0 as sinx = -cosx.
Dividing both sides by cosx gives us tanx = -1.
This tells us that the tangent of angle x is equal to -1. In a unit circle, this occurs at the angle 3π/4 (135 degrees) in the second quadrant and also at the angle -π/4 (-45 degrees) in the fourth quadrant.
So, the solutions for x that satisfy the equation sinx + cosx = 0 are x = 3π/4 + 2πn or x = -π/4 + 2πn where n is an integer.