даю 100 баллов алгебра
Ответы
Объяснение:
5.
2cosx-1=0 ; [-π;3π]
2cosx=1
cosx=1/2
x=π/3+2πk,k∈z
x= -π/3+2πk ,k∈z
-π<π/3+2πk<3π
-π-π/3<2πk<3π-π/3
-4π/3<2πk<8π/3
-2/3<k<4/3
k=0 ; x= π/3
k=1 ; x=π/3+2π=7π/3
x= -π/3+2πk ; k∈z
-π< -π/3+2πk<3π
-π+π/3<2πk<3π+π/3
-2π/3<2πk<10π/3
-1/3<k<5/3
k=0 ; x= -π/3
k=1 ; x= -π/3+2π=5π/3
ответ: π/3 ; 7π/3 ; -π/3 ; 5π/3
6. в условии не поняла с промежутком
если промежуток [ -π/2 ; π]
tg2x-1=0 ; [-π/2;π]
2x=π/2+πk,k∈z
x=π/4+πk/2,k∈z
x≠π/4+πk,k∈z
tg2x=1
2x=π/4+kπ,k∈z
x=π/8+πk/2 ; k∈z ; x≠π/4+πk/2 ; k∈z
x=π/8+πk/2 ; k∈z
-π/2<π/8+πk/2<π
-π/2-π/8<πk/2<π-π/8
-5π/8<πk/2<7π/8
-5/4<k<7/4
k= -1 ; x=π/8-π/2= -3π/8
k=0 ; x=π/8
k=1 ; x=π/8+π/2=5π/8
ответ: -3π/8 ; π/8 ; 5π/8
если промежуток [π/2 ; π]
tg2x-1=0
2x=π/2+πk,k∈z
x=π/4+πk/2,k∈z
x≠π/4+πk/2,k∈z
tg2x=1
2x=π/4+πk,k∈z
x=π/8+πk/2,k∈z ; x≠π/4+πk/2,k∈z
π/2<π/8+πk/2<π
π/2-π/8<πk/2<π-π/8
3π/8<πk/2<7π/8
3/4<k<7/4
k=0 ; x=π/8
k=1 ; x=π/8+π/2=5π/8
ответ: π/8 ; 5π/8