Решите тригонометрические уравнения:
1. 10sin²x - sin2x = 8cos² x
2. 1 - 6cos² x = 2sin 2x + cos 2x
1. 10sin²x - sin2x = 8cos² x
2. 1 - 6cos² x = 2sin 2x + cos 2x
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10sin²x - 2sinx·cosx - 8 + 8sin²x =0
18sin²x - 2sinx·cosx - 8sin²x - 8cos²x = 0
10sin²x - 2sinx·cosx - 8cos²x = 0
делим обе части на cos²x
10tg²x - 2tgx - 8 = 0
tgx = 1 tgx = - 4/5
x =π/4 + πk x = - arctg4/5 + πk