3sin^2x+7sinx×cosx=5​

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)