:1. 2sin^2x + 3cos^2x = 5sinx cosx 2. 2cos^2x + cosx = 1 3. 2cos^2 12x + 2 корень 2 cos 12x sin 12x + sin^2 12x = 0 4. 16sin x = cosx 5. cos^2x + 70sinx + 143 = 0 6. cos^2x + 23cosx = 24 7. cos^2x = 24cosx

2sin²x+3cos²x=5sinx*cosx |:cos²x
2tg²-5tgx+3=0
D=25-24=1
tgx=1.5; x1=arctg1.5+πn,n€Z
tgx=1; x2=-π/4+πn,n€Z

2) 2cos²x+cosx=1
2cos²x+cosx-1=0
пусть cosx=t(|t|≤1),имеем
2t²+t-1=0
t1=1/2; t2=-1
заменa
cosx=1/2 и cosx=-1
x1=±π/6+2πn; x2=2πn

3) 2cos²12x+2√2cos12xsin12x+sin²12x=0

tg²12x+2√2tgx+2=0
(tg12x+√2)=0
tg12x=-√2
x=-1/12arctg√2+πn/12

4)16sinx=cosx |:cosx
16tgx=1
tgx=1/16
x=arctg(1/16) + πn

далее аналогично, решать лень уже