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domain of y = ln( tan x ) and y = square root of (ln(sinx))

Domain of y = ln(tanθ)

The argument of a logarithm must be positive.

tanθ is non-negative in quadrants I and III.

The domain of y = ln(tanθ) is {θ: 0<θ<π/2 or π<θ<3π/2}.

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Domain of y = √ln(sinθ)

The argument of a logarithm must be positive, so 0<θ<π.

The radicand must be non-negative.

ln(sinθ) is positive for 0<θ<π.

The domain of y = √ln(sinθ) is {θ: 0<θ<π}.

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