Cos x = √6-7sin^2x+cos x.

Решение:

7sin² (5pi-x) - cos (3pi/2+x) cos (x-7pi) = 6

7sin² (pi-x) - sinxcos (pi-x) = 6

7sin²x+sinxcosx=6 (sin²x+cos²x)

7sin²x+sinxcosx-6sin²x-6cos²x=0

-6cos²x+sinxcosx+sin²x=0

-6+tgx+tg²x=0

tgx=y=>y²+y-6=0=>y1=2; y2=-3

1) tgx=2=>x=arctg2+pin

2) tgx=-3=>x=-arctg3+pik, n, k-целые.