# Avec calcul formel , la résolution de l'équation sqrt(sin(x)) + cos(x) = 1 est incorrecte

barakatomar1960 shared this question 2 years ago 1

Please post your file and the result you are expecting, as well your OS and GeoGebra version. 1

I think it's a bug (GGB-Algebra and/or GGB-CAS ).

Windows 10, GGB 5.0.553 1

I think that this equation needs to be solved in CAS.

GeoGebra problem is that it gives the extra solution in x=pi+2k pi, where the square root is not defined in R. 1

sqrt(sin(pi+2k pi))--->0 1

Oh, sorry!

I’ve misread the parenthesis, and thought that the square root contained both sine and cosine functions!

Damn. I need holidays :(

Have a nice Sunday, mathmagic,  1

directly from the help notes of the command

Sometimes you need to do some manipulation to allow the automatic solver to work, for example

sin(x)=(1-cos(x))^2

https://wiki.geogebra.org/e... 1

That’s clever!

And it works.

I’m wondering what went wrong with the original equation. Maybe something related to the period of the solutions?  1

Anyway, solving the equation “old style”, that is paper and pencil, the extra solution is pi +2k pi, and the other two are correct. 1

I think the problem is in continuity