A)sin²x+sinxcosx-2cos²x=0 /cos²x≠0
tg²x+tgx-2=0
tgx=a
a²+a-2=0
a1+a2=-1 U a1*a2=-2
a1=-2⇒tgx=-2⇒x=-arctg2+πn
a2=1⇒tgx=1⇒x=π/4+πn
б)sin²3x+3cos²3x+4cos3xsin3x=0 /cos²3x≠0
tg²3x+4tg3x+3=0
tg3x=a
a²+4a+3=0
a1+a2=-4 U a1*a2=3
a1=-3⇒tg3x=-3⇒3x=-arctg3+πn⇒x=-1/3arctg3+πn
a2=-1⇒tg3x=-1⇒3x=-π/4+πn⇒x=-π/12+πn
в)sin²x+2sinxcosx-3cos²x=0 /cos²x≠0
tg²x+2tgx-3=0
tgx=a
a²+2a-3=0
a1+a2=-2 U a1*a2=-3
a1=-3⇒tgx=-3⇒x=-arctg3+πn
a2=1⇒tgx=1⇒x=π/4+πn
г)sin²3x+5sin3xcos3x+4cos²3x=0 /cos²3x≠0
tg²3x+5tg3x+4=0
tg3x=a
a²+5a+4=0
a1+a2=-5 U a1*a2=4
a1=-4⇒tg3x=-4⇒3x=-arctg4+πn⇒x=-1/3arctg4+πn
a2=-1⇒tg3x=-1⇒3x=-π/4+πn⇒x=-π/12+πn