1
сos4x=0
4x=π/2+πn
x=π/8+πn/4,n∈z
2
√3sinx+cosx=0
2(√3/2sinx+1/2cosx)=0
2sin(x+π/6)=0
sin(x+π/6)=0
x+π/6=πn
x=-π/6+πn,n∈z
3
-√3tg(π-x)=1
√3tgx=1
tgx=1/√3
x=π/6+πn,n∈z
4
(1+cost)(√2sint-1)=0
cost=-1
t=π+2πn,n∈z
sint=1/√2
x=(-1)^n*π/4+πn,n∈z
5
2sin(3x-π/4)=-√2
sin(3x-π/4)=-√2/2
3x-π/4=-π/4+2πn U 3x-π/4=5π/4+2πn
3x=2πn U 3x=3π/2+2πn
x=2πn/3 ,n∈z U x=π/2+2πn/3,n∈z
6
2sin²x+3cosx=0
2-2cos²x+3cosx=0
cosx=a
2a²-3a-2=0
D=9+16=25
a1=(3-5)/4=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πn,n∈z
a2=(3+5)/4=2⇒cosx=2>1 нет решения
7
ctg(2π-x)-tg(3π/2+x)=2
-ctgx-ctgx=2
-2ctgx=2
ctgx=-1
x=3π/4+πn,n∈z