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?

The equation sin(9*x-(1/3)*Pi) = sin(7*x-(1/3)*Pi) can be solved easy by hand with solutions k*Pi and -Pi/48 + K*Pi/8. With Maple, I tried 
solve({sin(9*x-(1/3)*Pi) = sin(7*x-(1/3)*Pi)}, x, explicit, allsolutions)

I don't get the above solutions. How can I get these solutions?

Based on the equation at here https://www.mapleprimes.com/questions/209660-Problem-With-RealDomainsolve

I tried solve the equation (x-1)*sqrt(x^2 - 4)=0 in Real domain. My code
restart;
RealDomain:-solve((x-1)*sqrt(x^2-4) = 0, x);

I got there solutions are 1, 2, -2.  I think, If we solve the given in RealDomain, we only get two solutions -2 and 2.

My question is: How many solutions are there in the equation (x-1)*sqrt(x^2 - 4)=0 by RealDomain:-solve?

Two pictures by using Mathematica.

I am trying to find all real solutions of the system equations 
sol := solve(And(g'(x)=0,g''(x)<>0),x)   assuming real;
I tried

restart; fprime := x-> x^6-(3/2)*x^5+2*x^4+(5/2)*x^3-7*x^2+2:
f := unapply(simplify(int(fprime(x), x)), x):
g := unapply(expand(f(x^2+2*x)), x):
sol := solve(And(g'(x)=0,g''(x)<>0),x)   assuming real;
evalf(sol);

I don't get only real solutions. How can I get only real solutions?

How to get the only solution x = (1/6)*sqrt(114)*a of this equation?
restart;
with(Student:-MultivariateCalculus);
u := `<,>`(-(1/4)*a, -(1/12)*sqrt(3)*a, -x);
v := `<,>`(-(1/2)*a, (1/6)*sqrt(3)*a, (1/2)*x);
`assuming`([solve(Angle(u, v) = arccos(2*sqrt(26)*(1/13)), x)], [And(a > 0, x > 0)])