Arcsin((5x-1)/3)+2arccos((5x-1)/3)=5пи/6​

Question

Arcsin((5x-1)/3)+2arccos((5x-1)/3)=5пи/6​

Comments

Arcsin(x)+arccos(x) = pi/2 одз + остается один arccos

Answer 1

Ответ:х=0.5

Пошаговое объяснение:arcsin((5x-1)/3)+2arccos((5x-1)/3)=5π/6​

arccos((5x-1)/3)=π/2-arcsin((5x-1)/3), при условии  -1≤(5x-1)/3≤1;

-3≤(5x-1)≤3; -2≤5x≤4;-0.4≤x≤0.8;

arcsin((5x-1)/3)+2*(π/2-arcsin((5x-1)/3))=5π/6​

π-arcsin((5x-1)/3)=5π/6​

arcsin((5x-1)/3)=π/6​

(5x-1)/3=0.5

5x-1=1.5

5x=2.5

x=2.5/5

х=0.5∈ОДЗ.