Use properties of natural logarithms and fundamental trigonometric identities to show that the pair of expressions is equivalent. $$ln |1+ cos \theta| - 2 ln |sin \theta|$$ and $$- ln |1-cos \theta|$$ Rewrite the second term in the first expression using the power rule of logarithms. $$ln |1+ cos \theta| - 2 ln |sin \theta| = ln |1+ cos \theta| - ln$$
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Applying this rule to the term $$2 ln |sin \theta|$$, we get $$ln (|sin \theta|^2) = ln (sin^2 \theta)$$. Show more…
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