НОД (32;42)=2; б) НОД (54;72)=9; в) НОД(96;40)=8
Sina * cosa * sina/cosa = sin^2a
1дм³=1000см³
1000*10=10000см³+5см³=10005см³
1000*10=10000см³+50см³=10050см³
1000*10=10000см³+555см³=10555см³
1)10cos(2arctg(-1/2)
arctg(-1/2)=x;x€(-π/2;π/2)
tgx=-1/2
cos2x=?
1+tg²x=1/cos²x
cos²x=1/(1+tg²x)=1(1+1/4)=4/5
cos2x=2cos²x-1=8/5-1=3/5
10cos(2arctg(-1/2))=10*3/5=2*3=6
2)6√7(sin(arccos√2/3)=?
arccos√2/3=x;cosx=√2/3
x€(-π;π)
sinx=+√(1-2/9)=√7/3
6√7sin(arccos√2/3)=6*√7*√7/3=2*7=14
3)17cos(2arctg(-1/4))=?
arctg(-1/4)=x€(-π/2;π/2)
tgx=-1/4
1+tg²x=1/cos²x
cos²x=1/(1+1/16)=16/17
cos2x=2cos²x-1=2*16/17-1=(32-17)/17=15/17
17cos(2arctg(-1/4))=17*15/17=15
(7,43-2 3/25)+x=7
(7,43-2,12)+x=7
5,31+x=7
x=7-5,31
x=1,69
==========
(8,61-3 3/4)+y=12,1
(8,61-3,75)+y=12,1
4,86+y=12,1
y=12,1-4,86
y=7,24