1)
tg(arctg4x)=tg(π/4)
4x=1
[b]x=1/4[/b]
2)
tg(arctg3x)=tg(-π/3)
3x=-sqrt(3)
[b]x=-sqrt(3)/3[/b]
18.4
1)
cos(arccos(3x-2,5))=cos(2π/3)
3x-2,5=(-1/2)
3x=2
[b]x=2/3
[/b]
3)
cos(arccos(4-x))=cos(π/2)
4-x=0
[b]x=4[/b]
18.7
cos( arccos(3x^2-10x+2,5)=cos(2π/3)
3x^2-10x+2,5=-0,5
3x^2-10x+3=0
D=100-36=64
[b]x_(1)=1/3; x_(2)=3[/b]
3)
tg(arctg(x^2-9))=tg(arctg 8x)
x^2-9=8x
x^2-8x-9=0
D=64-4*(-9)=64+36=100
x_(1)=-1; x_(2)=9
1)
8*(arccox)^2+2π* (arccox)-π^2=0
D=(2π)^2-4*8*(-π^2)=36π^2
arccosx=-π/2 или arccosx=π/4
[b]x=0 [/b] или [b] x=sqrt(2)/2[/b]
2) arcsin2x-3arcsin x=0
arcsinx= α ⇒ sin α =x
arcsin2x= β ⇒ sin β =2x ⇒ sin β =2*sin α
arcsin2x-3arcsin x=0 ⇒ β -3 α =0 ⇒ β =3 α
sin β =2x ⇒ sin3 α =2x
sin α =x
sin3 α = 3 sin α -4 sin^3 α
2x=3*x-4x^3
4x^3-x=0
x*(4x^2-1)=0
x*(2x-1)*(2x+1)=0
x=0 или 2х-1=0 или 2х+1=0
[b]х=0 или х=1/2 или x=-1/2[/b]
Формулы: