Решите уравнения!!!!!sin^3 x - 7sinx cos^2 x-6cos^3 x=02cos4x-cos^3 x=2-16cos^2 x

Question

Решите уравнения!!!!!
sin^3 x - 7sinx cos^2 x-6cos^3 x=0

2cos4x-cos^3 x=2-16cos^2 x

Answer 1

1)(sin³x-sinxcos²x)-(6sinxcos²x+6cos³x)=0
sinx(sin²x-cos²x)-6cos²x(sinx+cosx)=0
sinx(sinx-cosx)(sinx+cosx)-6cos²x(sinx+cosx)=0
(sinx+cosx)(sin²x-sinxcosx-6cos²x)=0
sinx+cosx=0
sinx+sin(π/2-x)=0
2sinπ/4cos(x-π/4)=0⇒cos(x-π/4)=0⇒(x-π/4)=π/2+πn⇒x=3π/4+πn
sin²x-sinxcosx-6cos²x=0 /cos²x≠0
tg²x-tgx-6=0
tgx=a⇒a²-a-6=0⇒a1+a2=1 U a1*a2=-6⇒
a1=3⇒tgx=3⇒x=arctg3+πn
a2=-2⇒tgx=-2⇒x=-arctg2+πn