1.sin(-x/2) = √3/2
-sin(x/2) = √3/√2
-sin(x/2) = √6/2
sin(x/2) = -√6/2
Уравнение не имеет решений. x ∈ 0
2. cos(-3x) = √2/2
cos(3x)= √1
cos(3x) = 1
3x= 2πκ , κ ∈ Ζ
x= 2πκ/3 , κ ∈ Ζ
(3х(х-2))+(х+2)-4)/((х-2)(х+2)) = 0
(3х²-6х+х+2-4)/((х-2)(х+2)) = 0
(3х²-5х-2)/((х-2)(х+2)) = 0
ОДЗ: (х-2)(х+2)≠0; х≠-2; 2
3х²-5х-2=0
D=25+24=49
х₁=(5-7)/6=-1/3
х₂=(5+7)/6=2
3,5t+1-4t=7,5t-31; 3,5t-4t-7,5t= -31-1; -8t= -32; t=(-32)/(-8)=4. Ответ: t=4.
.............................дм
sin^2t cos^2t (tg^2 t + ctg^2 t+ 2)= 1
для наглядности разбью на действия
1)
2 = 1 + 1
ctg^2 t+ 1 = 1 / sin^2 t
tg^2 + 1 = 1 / cos^2
2)
1 / cos^2 + 1 / sin^2 t = ( sin^2 t + cos^2) / (sin^2t * cos^2t) = 1 /(sin^2t * cos^2t)
3)
sin^2t * cos^2t * 1 /(sin^2t * cos^2t) = (sin^2t * cos^2t) / (sin^2t * cos^2t) = 1