How do I answer this trig identity?

Question

ln|1+cos(theta)|+ln|1-cos(theta)| = 2ln|sin(theta)|

Answer 1

Remember that lnA + lnB = ln(AB), and 2lnA = ln(A²)

 

So ln|1+cosθ|+ln|1-cosθ| = 2ln|sinθ| = ln|(1 - cos²θ)| = ln|sin²θ|

 

Therefore, 1 - cos²θ = sin²θ.

 

This is an identity.  sin²θ + cos²θ = 1.

 

And can be proved using the Pythagorean Theorem.