5sin2x+12sin x cos x+4cos2x=0

Question

5sin2x+12sin x cos x+4cos2x=0

Answer 1

10Sinx Cos x + 12Sin xCos x + 4(Cos²x - Sin²x) = 0
22SinxCos x + 4Cos²x - 4Sin²x = 0 |: Cos²x≠ 0
22tg x + 4 - 4tg² x = 0 | : (-2)
2tg² x -11 tgx -2 = 0 
Решаем как квадратное:
 tgx =(11 +-√157)/4
 x = arctg (11 +-√157)/4