To solve this equation, we can first simplify the left side by using the properties of logarithms:

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

Now we can use the properties of logarithms to combine the terms:

lg(2tg x * cos x) = lg(sin x)

Set the arguments of both logarithms equal to each other:

2tg x * cos x = sin x

Now we can try to simplify the trigonometric expression by using identities:

2sin x / cos x * cos x = sin x
2sin x = sin x

This simplifies to:

2 = 1

Therefore, there seems to be an error in the calculation.