Ответы на вопрос:
x1 = arctg(5/2) + пk, (k - целое)
x2 = п/4 + пn, (n - целое)
Пошаговое объяснение:
3*(sin(x))^2 + 7*sin(x)cos(x) = 5
3*sin(x)^2 + 7*sin(x)cos(x) = 5(sin(x)^2 + cos(x)^2)
0 = 2*sin(x)^2 - 7*sin(x)cos(x) + 5*cos(x)^2 || : cos(x)^2
0 = 2*tg(x)^2 - 7*tg(x) + 5
Пусть tg(x) = t
2t^2 - 7t + 5 = 0
D = 49 - 4*2*5 = 49 -40 = 9
t1 = (7 + 3)/(2*2) = 10/4 = 2.5
t2 = (7 - 3)/(2*2) = 4/4 = 1
x1 = arctg(5/2) + пk, (k - целое)
x2 = arctg(1) + пn = п/4 + пn, (n - целое)
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