Решить триганометрические уравнения и неравенства. 15. 2sin^2 x + 3sinxcosx + cos^2 x = 0 16. cos^2 x - 3sinxcosx + 1 = 0 17. sinx + cosx = 1

2sin²x+3sinxcosx+cos²x=0/cos²x≠0
2tg²x+3tgx+1=0
tgx=a
2a²+3a+1=0
D=9-8=1
a1=(-3-1)/4=-1⇒tgx=-1⇒x=-π/4+πn
a2=(-3+1)/4=-1/2⇒tgx=-1/2⇒x=-arctg1/2+πn

cos²x-3sinxcosx+sin²x+cos²x=0/cos²x≠0
tg²x-3tgx+2=0
tgx=a
a²-3a+2=0
a1+a2=3 U a1*a2=2
a1=1⇒tgx=1⇒x=π/4+πn
a2=2⇒tgx=2⇒x=arctg2+πn

2sinx/2cosx/2+cos²x/2-sin²x/2-sin²x/2-cos²x/2=0
2sinx/2cosx/2-2sin²x/2=0/2cos²x≠0
tgx/2-tg²x/2=0
tgx/2(1-tgx/2)=0
tgx/2=0⇒x/2=πn⇒x=2πn
tgx/2=1⇒x/2=π/4+πn⇒x=π/2+2πn