I was briefly looking at this and decided to remove all the underscores. That should be harmless of course.
Then tested my answer to your previous question, but now I got 94 solutions instead of 90. Weird!
I used Edit/ Find/Replace in Maple.  For the record, here is the code with the underscores removed:
restart;
S := Matrix( [ [a1, a2, a3, a4], [b1, b2, b3, b4], [c1, c2, c3, c4], [d1, d2, d3, d4] ] );
eq1:=a1*d1 = b1*c1, a2*d2 = b2*c2, a3*d3 = b3*c3, a4*d4 = b4*c4;
R := Matrix( [ [s1, t1, r1, l1], [s2, t2, r2, l2], [s3, t3, r3, l3], [s4, t4, r4, l4] ] );
eq2:=s1*l1 = t1*r1,s2*l2 = t2*r2,s3*l3 = t3*r3,s4*l4 = t4*r4;
T := Matrix( [ [1, 0, 0, 1], [0, 1, 0, 0], [0, 1, 0, 0], [1, 0, 0, 1] ] );
S.R=~T;
convert(%,set);
res:=solve(% union {eq1,eq2});
nops([res]);
res[1];

Could you give us the expression you want to minimize? In text here or as an uploaded worksheet.

restart;
sys := [diff(y(x), x) = -(4*cos(x)*y(x)+z(x)*cos(x)^2+3*z(x))/(sin(x)*(cos(x)^2-9)),
diff(z(x), x) = -(y(x)*cos(x)^2+3*y(x)+4*z(x)*cos(x))/(sin(x)*(cos(x)^2-9))];

normal(sys[1]+sys[2]);
#Letting u = y+z:
eqS:=eval(%,{z=0,y=u});
U:=dsolve(eqS) assuming real;
normal(sys[1]-sys[2]);
#Letting v = y-z:
eqD:=eval(%,{z=0,y=v});
dsolve(eqD) assuming real;
V:=subs(_C1=_C2,%);
y(x)=rhs((U+V)/2);
z(x)=rhs((U-V)/2);

@Markiyan Hirnyk I noticed that the right hand sides of sys shared singularities defined by sin(x) = 0.
Thus the variable change from x to t given by diff(x(t),t)=sin(x(t)) seemed natural because the ode system in X(t), Y(t) would be without singularities (by the chain rule dy/dt = (dy/dx)*(dx/dt)=(dy/dx)*sin(x) ).
Omitting the last line in my comment above and setting
res:= collect(%,[_C1,_C2],normal);
#the solutions can be extended to all of R by

res2:=eval(res,{(1+cos(x))^(-1/2)=1/(sqrt(2)*cos(x/2)),sqrt(1+cos(x))=sqrt(2)*cos(x/2)});
odetest(res2,sys); #Checking
y1,z1:=op(eval(subs(res2,[y(x),z(x)]),{_C1=1,_C2=0}));
y2,z2:=op(eval(subs(res2,[y(x),z(x)]),{_C1=0,_C2=1}));
plot([y1,y2,z1,z2],x=0..4*Pi);

Since you left sol1[2] to the MaplePrimes users I thought I might try a variant of the idea.

restart;
sys := [diff(y(x), x) = -(4*cos(x)*y(x)+z(x)*cos(x)^2+3*z(x))/(sin(x)*(cos(x)^2-9)),
diff(z(x), x) = -(y(x)*cos(x)^2+3*y(x)+4*z(x)*cos(x))/(sin(x)*(cos(x)^2-9))];
#Making the change of variable given by sin(x)*diff(y,x) = diff(y,t),
# i.e. diff(x(t),t)=sin(x(t)) and choosing x(0) = Pi/2:  
int(1/sin(x1),x1=Pi/2..x, AllSolutions) assuming x>0,x<Pi;
St:=t=combine(%) assuming x>0,x<Pi;
dsolve({diff(x(t),t)=sin(x(t)),x(0)=Pi/2});
Sx:=subs(x(t)=x,%);
PDEtools:-dchange({Sx,y(x)=Y(t),z(x)=Z(t)},sys,[t,Y,Z]):
sys2:=combine(solve(%,{diff(Y(t),t),diff(Z(t),t)}));
tres:=dsolve(sys2) assuming t>0;
PDEtools:-dchange({St,Y(t)=y(x),Z(t)=z(x)},tres,[x,y,z]):
simplify(%) assuming real;
collect(%,[_C1,_C2],normal);
subs(sin(x)=sqrt(1-cos(x))*sqrt(1+cos(x)),%);

@matja There must have been something else interfering with the assume command since the following works:

restart;
assume(a>0);
limit(exp(-a*x), x = infinity);

@matja There must have been something else interfering with the assume command since the following works:

restart;
assume(a>0);
limit(exp(-a*x), x = infinity);

Certainly S1+S2 is the sum of the two expressions, so I don't know what your problem is. Do you want to use simplify, expand, or combine on the sum or what?

An animation:

plots:-animate(plot, [S, theta = 0 .. 10], t = 0 .. 1, frames = 100);

The sum in S1 is the first few terms of

Sum(cos((2*k+1)*theta)/(2*k+1)*(-1)^k,k=0..infinity);

which is the Fourier series of

f:=piecewise(abs(theta)<Pi/2,Pi/4,-Pi/4);

restart;
eq1:=eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10);
eq2:=eval((1+I*i*Pi)*x*sin(x)-I*i*Pi*cos(x), i = 10);
res:=RootFinding:-Analytic(eq2, x = -20-I .. 20+I);
nops([res]);
#Check:
evalf(eval~(eq1,x=~[res]));
simplify(fnormal(%,8));

restart;
eq1:=eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10);
eq2:=eval((1+I*i*Pi)*x*sin(x)-I*i*Pi*cos(x), i = 10);
res:=RootFinding:-Analytic(eq2, x = -20-I .. 20+I);
nops([res]);
#Check:
evalf(eval~(eq1,x=~[res]));
simplify(fnormal(%,8));

@Markiyan Hirnyk By doing successively

RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -20-I .. 20+I);
RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -20-I .. 20+I,continue);

you find 6 roots.

@Markiyan Hirnyk By doing successively

RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -20-I .. 20+I);
RootFinding:-Analytic(eval(x*tan(x)-I*i*Pi/(1+I*i*Pi), i = 10), x = -20-I .. 20+I,continue);

you find 6 roots.

You are more likely to get an answer if you give us the text instead of an image.

Which parameter values will make it run? 
Maybe an uploaded worksheet will help.

Which parameter values will make it run? 
Maybe an uploaded worksheet will help.