3sinx=2ctgx + (2/sinx) Решите

3sinx=2ctgx + (2/sinx) |*sinx

3sin^2x=2ctgx*sinx+2

3sin^2x-2ctgx*sinx=2

3sin^2x-2cosx=2

3 (1-cos^2x) - 2cosx=2

3-3cos^2x-2cosx-2=0

-3cos^2x-2cosx+1=0 | * (-1)

3cos^2x+2cosx-1=0

Пусть cos^2x=t, тогда:

3t^2+2t-1=0

D=4+1*3*4=16

t1=-2+4/6=2/6=1/3

t2=-2-4/6=-1

cos^2x=1/3

x = (-1) ^K*arccos (1/3) + pik

cos^2x=-1

x=pik