7 sin² x-8 sin x cos x =15cos² x

Question

7 sin² x-8 sin x cos x =15cos² x

Answer 1

7 sin² x-8 sin x cos x -15cos² x = 0 | : Cos²x≠0
7 tg² x - 8tgx -15 = 0
Решаем как квадратное
D = b² - 4ac = 64 - 4*7*(-15) = 484
a)tgx = (8+22)/14 = 30/14 = 15/7
х = arctg(15/7) + π к, к∈Z
б) tgx = (8 - 22)/14 = -1
х = -π/4 + πn, n ∈Z