Question

Помогите пожалуйста с тригонометрией! Срочно! cosx+sinx+sin2x+1=0

Answer 1

cosx+2sinxcosx+sinx=-1
cos²x+2sinxcosx+sin²x-1+cosx+sinx=-1
(cosx+sinx)²+(cosx+sinx)=0
(cosx+sinx)(cosx+sinx+1)=0
1)cosx+sinx=0
разделим обе части уравнения на cosx(cosx≠0)
1+tgx=0
tgx=-1
x=-π/4+πn
2)cosx+sinx+1=0
cosx+sinx=-1
разделим обе части уравнения на √2
√2cosx/2+√2sinx/2=-√2/2
cosxcosπ/4+sinxsinπ/4=-√2/2
cos(x-π/4)=-√2/2
x-π/4=+-3π/4+2πn
а)x=-π/2+2πn
б)x=π+2πn

Answer 2

(cosx+sinx)+(cosx+sinx)²=0
(cosx+sinx)(1+cosx+sinx)=0
cosx+sinx=0|cosx≠0
1+tgx=0
tgx=-1⇒x=-π/4+πn
1+cosx+sinx=0
2cos²x/2+2sinx/2*cosx/2=0
2cosx/2*(cosx/2+sinx/2)=0
cosx/2=0
x/2=π/2+πn⇒x=π+2πn
cosx/2+sinx/2=0|cosx/2≠0
1+tgx/2=0
tgx/2=-1⇒x/2=-π/4+πn⇒x=-π/2+2πn