Question

Hi,

I need to establish an identity starting with the left side

ln |sec theta| = -ln | cos theta|

help?

Answer 1

Here are the steps,
\[\ln (\sec (\theta))=-\ln (\sec (\theta))\]\[e ^{\ln \sec \theta}=e^{-\ln (\sec (\theta))}\]\[\sec(\theta)=1/\cos (\theta)\]\[1/\cos (\theta)=1/\cos (\theta)\]\[1=1\]