# How do you rewrite the expression as a single logarithm and simplify lnabs(secx)+lnabssinx?

Jan 13, 2017

Use the property $\ln \left(a\right) + \ln \left(b\right) = \ln \left(a b\right)$
$\ln | \sec \left(x\right) | + \ln | \sin \left(x\right) | = \ln | \sec \left(x\right) \sin \left(x\right) |$
Use the identity $\sec \left(x\right) \sin \left(x\right) = \tan \left(x\right)$
$\ln | \sec \left(x\right) | + \ln | \sin \left(x\right) | = \ln | \tan \left(x\right) |$