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 x2sin x = sin x
This simplifies to:
2 = 1
Therefore, there seems to be an error in the calculation.
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.