4sin^2 x\2- cos^2 x\2=1,5 + sinx

Решим уравнение.

4 * sin^2 (x/2) - cos^2 (x/2) = 1,5 + sin x; 

4 * sin^2 (x/2) - cos^2 (x/2) - 1,5 - sin x = 0;  

4 * sin^2 (x/2) - (1 - sin^2 (x/2)) - 1,5 * (sin^2 (x/2) + cos^2 (x/2)) - 2 * sin (x/2) * cos (x/2) = 0; 

4 * sin^2 (x/2) - 1 + sin^2 (x/2) - 1,5 * sin^2 (x/2) - 1.5 * cos^2 (x/2) - 2 * sin (x/2) * cos (x/2) = 0;  

Приведем сходственные значения. 

3,5 * sin^2 (x/2) - sin^2 (x/2) - cos^2 (x/2) - 1.5 * cos^2 (x/2) - 2 * sin (x/2) * cos (x/2) = 0;  

2.5 * sin^2 (x/2)  -  2.5 * cos^2 (x/2) - 2 * sin (x/2) * cos (x/2) = 0;  

5 * sin^2 (x/2)  -  5 * cos^2 (x/2) - 4 * sin (x/2) * cos (x/2) = 0;  

5 * tg^2 (x/2) - 4 * tg (x/2) - 5 = 0; 

tg (x/2) = 0.4 - 0.229; 

tg (x/2) = 0.4 + 0.229; 

x/2 = arctg (0.4 - 0.229) + pi * n; 

x/2 = arctg (0.4 + 0.229) + pi * n;  

x = 2 * arctg (0.4 - 0.229) + pi * n; 

x = 2 * arctg (0.4 + 0.229) + pi * n.