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

lg^2 (tg^2 x) + lg (cos x) = lg (sin x)

Область определения:

{ sin x > 0

{ cos x > 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 степени из 10

x2 = arctg (10^ (1/4)) + pi*k

С учетом Обл. Опр. x2 = arctg (10^ (1/4)) + 2pi*k