Natural log and trigonometry

Algebra Level 3

Consider the following equations

ln(sinx)+ln(cosx)=1ln(sinx+cosx)=12(ln(y+e)1)\begin{aligned} \ln(\sin x)+\ln(\cos x)&=-1\\ \ln(\sin x+\cos x)&=\frac{1}{2}(\ln(y+e)-1) \end{aligned}

Find the value of yy.

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