Sin²x + 14sinxcosx = 15cos²x

Sin²x+14sinxcosx=15cos²x

sin²x+14sinxcosx-15cos²x=0 |: cos²x

tg²x+14tgx-15=0

Обозначим: tgx = t тогда

t²+14t-15=0

D = 196+60 = 256

t₁ = - 14+16/2 = 1

t₂ = - 14-16/2 = - 15

1) tgx = 1

x = π/4+πn, n∈z

2) tgx = - 15

x = arctg (-15) + πn

x = - arctg15+πn, n∈z