Sin^2*x+9cos^2*x=5sin2x

sin^2*x+9cos^2*x=5 (2sinx*cosx)

sin^2*x+9cos^2*x-10sinx*cosx=0

(sin^2*x) / cos^2*x + (9cos^2*x) / cos^2*x - (10sinx*cosx) / cos^2*x=0

tg^2*x+9-10tgx=0

Пусть tgx=t

t^2+9-10t=0

D = 100-36=64

x 1 и 2 = (10+-8) / 2=9 и 1

tgx=9 and tgx=1

x = arctg9+пиk and x=пи/4+пиN