y=ln sqrt((1+sin x)/(1-sin x))

Apply Logarithm Property: We are given the equation y = ln(sqrt((1+sin x)/(1-sin x))). To simplify this, we can use the property of logarithms that states ln(a^(1/2)) = (1/2)ln(a).Simplify Expression: Apply the logarithm property to the equation: y = (1/2)ln((1+sin x)/(1-sin x))Final Result: Now we have a simplified expression for y in terms of x. There is no further simplification or solving needed, as we have expressed y as a function of x.

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$y=\ln \sqrt{\left(\frac{1+\sin x}{1-\sin x}\right)}$

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y=\ln \sqrt{\left(\frac{1+\sin x}{1-\sin x}\right)}

Apply Logarithm Property: We are given the equation $y = \ln(\sqrt{(1+\sin x)/(1-\sin x)})$ . To simplify this, we can use the property of logarithms that states $\ln(a^{1/2}) = (1/2)\ln(a)$ .
Simplify Expression: Apply the logarithm property to the equation: $\newline$ $y = \frac{1}{2}\ln\left(\frac{1+\sin x}{1-\sin x}\right)$
Final Result: Now we have a simplified expression for $y$ in terms of $x$ . There is no further simplification or solving needed, as we have expressed $y$ as a function of $x$ .