Решите уравнения!

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

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

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