4sin^2+3Sinx*cosx-cosx^2x=0
4sin^2x+3Sinx*cosx-cosx^2x=0 делим всё на cosx^2x≠0
4tg^2x+3tgx-1=0
Замена tgx=t, t∈(-∞;+∞)
4t^2+3t-1=0
D=9+16=25
t=(-3+5)/8 = 1/4
t=(-3-5)/8 = -1
tgx = 1/4⇒ x=acrtg(1/4)+pik, k∈Z
tgx = -1⇒ x= -pi/4+pik, k∈Z
ОТВЕТ:
acrtg(1/4)+pik, k∈Z
-pi/4+pik, k∈Z