Задача 26984 4.49) arcsin(x^2-x+1/sqrt(2)) =...

slava191

02.05.2018

4.49) arcsin(x^2-x+1/sqrt(2)) = arccos(x^2-x+1/sqrt(2))

SOVA

02.05.2018

★

Так как
arcsin(x^2–x+(1/√2)) + arccos(x^2–x+(1/√2))=Pi/2 ⇒
arccos(x^2–x+(1/√2))=Pi/2 - arcsin(x^2–x+(1/√2))

arcsin(x^2–x+(1/√2)) = Pi/2 - arcsin(x^2–x+(1/√2))
2arcsin(x^2–x+(1/√2)) = Pi/2
arcsin(x^2–x+(1/√2)) = Pi/4
sin( arcsin(x^2–x+(1/√2))) = sin(Pi/4)
Так как sin(arcsina)=a

x^2–x+(1/√2)=1/√2
x^2-x=0
x*(x-1)=0
x=0 или х=1
О т в е т. 0; 1