9sinxcosx-7cos^2x=2sin^2x

Question

9sinxcosx-7cos^2x=2sin^2x

Answer 1

2 sin^2 x - 9 sinx * cos x + 7 cos^2 x = 0;   /:cos^2≠0;
2 tg^2 x - 9 tgx + 7 = 0;
tg x = t;
 2t^2 - 9t + 7 = 0;
 t1 = 1;  tgx = 1; ⇒ x = π/4  + π*k;  k∈Z;
 t2 =7/2;  tg x= 7/2; ⇒ x = arctg(7/2) + π*k; k∈Z