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**1. The problem statement, all variables and given/known data**

[tex]\int \frac{cos(x) + sin(x)}{sin(2x)}dx[/tex]

**2. Relevant equations**

Not sure if it led me astray, but I used the trig. property:

[tex]sin(2x) = 2sin(x)cos(x)[/tex]

**3. The attempt at a solution**

[tex]= \int \frac{cos(x) + sin(x)}{2sin(x)cos(x)}dx[/tex]

[tex]= 1/2 \int(csc(x) + sec(x))dx[/tex]

[tex]= 1/2ln|csc(x) - cot(x)| + 1/2ln|sec(x) + tan(x)| + C[/tex]

[tex]= 1/2 ln|csc(x)sec(x) + sec(x) - csc(x) - 1| + C[/tex]

I feel like this is wrong, but not sure where I'm messing up. Maybe my trig. property isn't the way to go.