Сподробным решением. 1) 5sinx+6cosx=6 2)3sin^2x+sinxcosx=2cos^2x

1)10six/2cosx/2+6cos²x/2-6sin²x/2-6sin²x/2-6cos²x/2=0
-12sin²x/2+10sinx/2cosx/2=0/cos²x/2≠0
12tg²x/2-10tgx/2=0
tgx/2(12tgx/2-10)=0
tgx/2=0⇒x/2=πn⇒x=2πn
tgx/2=5/6⇒x/2=arctg5/6+πn⇒x=2arctg5/6+2πn
2)3sin²x+sinxcosx-2cos²x=0/cos²x≠0
3tg²x+tgx-2=0
tgx=a
3a²+a-2=0
D=1+24=25
a1=(-1-5)/6=-1⇒tgx=-1⇒x=-π/4+πn
a2=(-1+5)/6=2/3⇒tgx=2/3⇒x=arctg2/3+πn