Solve 1/2ln|1+sinx|+1/2ln|1-sinx|

$$\frac { 1 } { 2 } \ln | 1 + \sin x | + \frac { 1 } { 2 } \ln | 1 - \sin x |$$

Factor

$$\frac{\ln(\sin(x)+1)+\ln(-\sin(x)+1)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\ln(|1+\sin(x)|)+\ln(|1-\sin(x)|)}{2\ln(e)}$$

Consider \frac{1}{\ln(e)}\left(\ln(|1+\sin(x)|)+\ln(|1-\sin(x)|)\right). Factor out \frac{1}{\ln(e)}.

$$\frac{\ln(|1+\sin(x)|)+\ln(|1-\sin(x)|)}{\ln(e)}$$

Rewrite the complete factored expression.

$$\frac{\ln(|1+\sin(x)|)+\ln(|1-\sin(x)|)}{2\ln(e)}$$

Evaluate

$$\frac{\ln(\sin(x)+1)+\ln(-\sin(x)+1)}{2}$$