Question

1. Sa se rezolve in R ecuatia: arcsin 2x = -1/2.
2. Sa se rezolve ecuatia: arcsin 1/2 + arccos x = pi/2 , x apartine intervalului [-1;1].
3. Sa se rezolve ecuatia: arcsin x + arccos 1/(radical din 2) = pi/2.

Answer 1

arcsin:[-1,1]→[-π/2,π/2] : arccos:[-1,1]→[0.π]
1)arcsin2x=-1/2 =>2x=-π/6 =>x=-π/12
2) arcsin1/2=π/6 ecuatia devine
π/6+arccosx=π/2
arccosx=π/2-π/6
arccosx=π/3  =>x=1/2
3)1/√2  =√2/2  Ecuatia  devine
arcsinx+arccos√2/2=π/2 =>
arcsinx+π/4=π/2
arcsinx=π/2-π/4=π/4