3
[tgx-8=0⇒tgx=8⇒x=arctg8+πk,k∈z
[4cos3x+2=0⇒cos3x=-1/2⇒3x=+-2π/3+2πk⇒x=+-2π/9+2πk/3,k∈z
4
2sin2xcos2x+2cos²2x=0
2cos2x(sin2x+cos2x)=0
cos2x=0⇒2x=π/2+πk⇒x=π/4+πk/2,k∈z
sin2x+cos2x=0/cos2x
tg2x+1=0⇒tg2x=-1⇒2x=-π/4+πk⇒x=-π/8+πk/2,k∈z
5
sin(7x)-sin(π/2-12x)=0
2sin(19x/2-π/4)cos(π/4-5x/2)=0
sin(19x/2-π/4)=0
19x/2-π/4=πk
19x/2=π/4+πk
x=π/38+2πk/19,k∈z
cos(π/4-5x/2)=0
5x/2-π/4=π/2+πk
5x/2=3π/4+πk
x=3π/10+2πk/5,k∈z
6
2sin²x+2cos²x+14cos²x-12sinxcosx=0
2sin²x-12sinxcosx+16cos²x/2cos²x
tg²x-6tgx+8=0
tgx=t
t²-6t+8=0
t1=2⇒tgx=2⇒x=arctg2+πk,k∈z
t2=4⇒tgx=4⇒x=arctg4+πk,k∈z