1- cos (∏-x) + sin (∏/2+x/2) = 0

1 - (-cosx) +  cos x/2 = 0

(1 + cos x) + cos x/2 = 0

2cos² x/2  + cos x/2 = 0

cos x/2 ( 2cos x/2  + 1) = 0

1) cos x/2 = 0   -->   x/2 = ∏/2 + ∏k;  

    x = ∏+2∏k,   k C Z

2) 2cos x/2 = -1  ->  cos x/2 = -1/2;   x/2 = ±(∏ - ∏/3) + 2∏n;  

    x = ± 4∏/3 + 4∏n,  n C Z.