12Sin²x + 7Sin2 x -8 = 0
12Sin²x + 14SinxCos x -8·1 = 0
12Sin²x + 14SinxCosx -8(Sin²x+ Cos²x) = 0
12Sin²x + 14SinxCos x -8Sin²x -8Cos²x = 0
4Sin²x + 14Sin xCos x -8 Cos²x = 0 | :Cos²x
4tg² + 14tgx -8=0
2tg²x + 7tgx -4 = 0
Решаем как квадратное
D = b²-4ac = 49 -4·2·(-4) =81
a) tgx = (-7+9)/4 = 2/4 = 1/2
x = arc tg(1/2) + πk, k∈Z
б) tg x = (-7-9)/4 = -4
x = =arctg4 + πn, n∈Z