2sin²x+5cosx-4=0
2-2cos²x+5cosx-4=0
cosx=a
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=1/2⇒cosx=1/2⇒x=+-π/3+2πn,n∈z
a2=(5+3)/4=2⇒cosx=2>1 нет решения
2tgx-ctgx-1=0
2tgx-1/tgx-1=0
2tg²x-1-tgx=0,tgx≠0
tgx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒tgx=-1/2⇒x=-arctg1/2+πn,n∈z
a2=(1+3)/4=1⇒tgx=1⇒x=π/4+πn,n∈z
6sin²x-4sin2x=-1
6sin²x-8sinxcosx+sin²x+cos²x=0/cos²x
7tg²x-8tgx+1=0
tgx=a
7a²-8a+1=0
D=64-28=36
a1=(8-6)/14=1/7⇒tgx=1/7⇒x=arctg1/7+πn,n∈z
a2=(8+6)/14=1⇒tgx=1⇒x=π/4+πn,n∈z