lg^2 (tg^2x)+lg(cosx)=lg(sinx)

lg^2 (tg^2 x) + lg (cos x) = lg (sin x)
Область определения:
sin x gt; 0
cos x gt; 0
x (2pi*k; pi/2+2pi*k)
[lg (tg^2 x)]^2 = lg (sin x) - lg (cos x)
[2lg (tg x)]^2 = lg (sin x/cos x) = lg (tg x)
4[lg (tg x)]^2 - lg (tg x) = 0
lg (tg x)*(4lg (tg x) - 1) = 0
1) lg (tg x) = 0
tg x = 1
x1 = pi/4 + pi*n
С учетом Обл. Опр. x1 = pi/4 + 2pi*n
2) 4lg (tg x) - 1 = 0
lg(tg x) = 1/4 = lg(10^(1/4))
tg x = 10^(1/4) = корень 4 ступени из 10
x2 = arctg (10^(1/4)) + pi*k
С учетом Обл. Опр. x2 = arctg(10^(1/4)) + 2pi*k