cos²x-sinxcosx+cosx-sinx=0
cosx(cosx-sinx)+(cosx-sinx)=0
(cosx-sinx)(cosx+1)=0
cosx-sinx=0/cosx
1-tgx=0
tgx=1
x=π/4+πn,n∈z
cosx=-1⇒x=π+2πk,k∈z
π/2≤π/4+πn≤2π
2≤1+4n≤8
1≤4n≤7
1/4≤n≤7/4
n=1⇒π/4+π=5π/4
π/2≤π+2πk≤2π
1≤2+4k≤4
-1≤4k≤2
-1/4≤k≤1/2
k=0⇒x=π
Пошаговое объяснение:
cos²x-sinxcosx+cosx-sinx=0
cosx(cosx-sinx)+(cosx-sinx)=0
(cosx-sinx)(cosx+1)=0
cosx-sinx=0/cosx
1-tgx=0
tgx=1
x=π/4+πn,n∈z
cosx=-1⇒x=π+2πk,k∈z
π/2≤π/4+πn≤2π
2≤1+4n≤8
1≤4n≤7
1/4≤n≤7/4
n=1⇒π/4+π=5π/4
π/2≤π+2πk≤2π
1≤2+4k≤4
-1≤4k≤2
-1/4≤k≤1/2
k=0⇒x=π
cos²x-sinxcosx+cosx-sinx=0
cosx(cosx-sinx)+(cosx-sinx)=0
(cosx-sinx)(cosx+1)=0
cosx-sinx=0/cosx
1-tgx=0
tgx=1
x=π/4+πn,n∈z
cosx=-1⇒x=π+2πk,k∈z
π/2≤π/4+πn≤2π
2≤1+4n≤8
1≤4n≤7
1/4≤n≤7/4
n=1⇒π/4+π=5π/4
π/2≤π+2πk≤2π
1≤2+4k≤4
-1≤4k≤2
-1/4≤k≤1/2
k=0⇒x=π
Пошаговое объяснение: