3cos²x - 5cosx - 8 = 0
cosx = t, -1≤x≤1
3t² - 5t - 8 = 0 t = -1 , t = 8/3>1
cosx = -1
x = π + 2πk; k - целое
10sin²x - sin2x = 8cos²x
10sin²x - 2sinx·cosx - 8 + 8sin²x =0
18sin²x - 2sinx·cosx - 8sin²x - 8cos²x = 0
10sin²x - 2sinx·cosx - 8cos²x = 0 однородное уравнение 2 степени, делим обе части на cos²x
10tg²x - 2tgx - 8 = 0
tgx = 1 tgx = - 4/5
x =π/4 + πk x = - arctg4/5 + πk
7 = 7sin2x - 9cos2x
7sin²x + 7cos²x = 14sinx·cosx - 9cos²x + 9sin²x
2sin²x - 16cos²x +14sinx·cosx =0
2tg²x +14tgx - 16 =0
tgx = 1 tgx = - 8
x = π/4 +πk x= - arctg8 + πk