Question

若arcsinx+arcsiny=2π/3 并且 arccosx - arcosy = π/3, 求x及y的值.

Answer 1

(因为 arcsinx+arccosx=π/2 arcsiny+arccosy=π/2) arccosx - arcosy = π/3arcsinx+arcsiny=2π/3 相加得到arccosx - arcosy +arcsinx+arcsiny=π

arcsiny-arcosy=π/2

arcsiny+arccosy=π/2 得到arcsiny=π/2 y=1

arcsinx+arcsiny=2π/3arcsinx+π/2=2π/3 得到arcsinx=π/6 x=1/2