3sin 2x+2sin (П/2+2x) = 3
3sin2x+2cos2x=3
6sinxcosx+2(1-2sin^2x)=3(sin^2x+cos^2x)
-7sin^2x+6sinxcosx-3cos^2x=-2
5sin^2x-6sinxcosx+cos^2x=0 /:cos^2x≠0
5tg^2x-6tgx+1=0
D=16>0
tgx=1⇒x=pi/4+pik, k∈Z
tgx=1/5⇒x=arctg1/5+pin, n∈Z
ОТВЕТ: pi/4+pik, k∈Z
arctg1/5+pin, n∈Z
3sin 2x+2sin (П/2+2x) = 3
3sin2x+2cos2x=3
6sinxcosx+2(1-2sin^2x)=3(sin^2x+cos^2x)
-7sin^2x+6sinxcosx-3cos^2x=-2
5sin^2x-6sinxcosx+cos^2x=0 /:cos^2x≠0
5tg^2x-6tgx+1=0
D=16>0
tgx=1⇒x=pi/4+pik, k∈Z
tgx=1/5⇒x=arctg1/5+pin, n∈Z
ОТВЕТ: pi/4+pik, k∈Z
arctg1/5+pin, n∈Z