arcsina+arccosa+arcga=[blue][b](π/2)+arctga[/b][/blue]
[red]|a| ≤ 1[/red]⇒ -1 ≤ a ≤ 1 ⇒ arctg(-1) ≤ arctga ≤ arctg1
⇒
(-π/4) ≤ arctga ≤(π/4)
Тогда
[b]π/4[/b]=(π/2)- (π/4) ≤ [blue][b]arcsina+arccosa+arcga[/b] [/blue]≤(π/2)+ (π/4)=3π/4
Наименьшее [b]π/4[/b]