Решите1+3sin^2x=4sinxcosx

Question

Решите1+3sin^2x=4sinxcosx

Answer 1

1+3sin^2x=4sinxcosx
sin^2x+cos^2x+3sin^2x-4sinxcosx=0
4sin^2x-4sinxcosx+cos^2x=0  |: cos^2x
4tg^2x-4tgx+1=0
tgx=a
4a^2-4a+1=0
a=1/2
tgx=1/2
x=arctg1/2+pi*n, n∈Z