Solve Trig Eqn: Find & Combine 2 Solutions for x

[primarygun]

General solution for a trigonometry equation.
I solved this equation with several method and I found two possible expressions for the answers. They should be exactly the same. Please help me check for them or combine them together to give the one which is more common. Thanks for any ideas.
$\cos x + \sin x=0$
$x=n\pi -\pi/4$
$x=(n\pi)/2+\pi/4$

 

[arildno]

Your first is correct.
Letting n be some integer, another way to write the solutions is:
$$x=\frac{2n+1}{2}\pi+\frac{\pi}{4}$$
Your last equation is incorrect; set n=2.
This says that $$x=\frac{5\pi}{4}$$ is a root; but this is untrue, since it lies in the 3.quadrant where both the sine and cosine functions are negative.

 

[primarygun]

Oh sorry, I missed to state that the n for the second expression is any odd integer. Really sorry.

 

[arildno]

Oh sorry, I missed to state that the n for the second expression is any odd integer. Really sorry.

In that case, of course, your second equation is just the one I provided; both 1) and 2) are standard ways of writing the solutions

 

[primarygun]

Thank you very much.