.....................................
Tg 15 · tg 30 · tg 60 · tg 75 =
= (tg 15· tg 75) · (tg 30 · tg 60) =
= (tg 15· ctg 15) · (tg 30 · ctg 30) =
= 1 · 1 = 1
Sinx=0.5√2
x=(-1)^k*π/4+πk, k € Z
2) 2sin²x-cosx-1=0
2-2cos²x-cosx-1=0
2cos²x+cosx-1=0
Пусть cosx=t(|t|≤1)
2t²+t-1=0
D=1+8=9
t1=(-1+3)/4=1/2
t2=(-1-3)/4=-1
замена
cosx=1/2
x=±π/3+2πn, n € Z
cosx=-1
x=±π+2πn, n € Z
3)sin²x-2sinxcosx-3cos²x=0|:cos²x
tg²x-2tgx-3=0
D=4+12=16; √D=4
tgx=-1
x=-π/4+πn, n € Z
tgx=3
x=arctg3+πn, n € Z