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Question: Bugs with RealDomain:-solve ?

Question:Bugs with RealDomain:-solve ?

minhthien2016 370 Maple 2018
solve realdomain
July 22 2019
1

I want to solve the equation (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0 in RealDomain. I tried
 

restart; 
RealDomain:-solve({(-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, {x});

I got four solutions

If I work around

restart;
 RealDomain:-solve({-x^2+4*x > 0, (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, x);

I only got two solutions

With Mathematica, I got three solutions 

That is mean, Maple lost the solution x = 5*Pi/4. I check this thing

f:= x-> (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(4*x-x^2) ;
f(5*Pi/4);

and got the result 0. 

Are these bugs?
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