How do you rewrite the expression as a single log and simplify ln|sin θ| - ln|cos θ|?

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How do you rewrite the expression as a single log and simplify ln|sin θ| - ln|cos θ|?

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Answer 1 · 2016-06-12T03:34:51

Combine ln terms and then the trig terms to get #ln(|tantheta|)#

Explanation:

Let's first look at the original:

#ln|sintheta|-ln|costheta|#

The first thing we can do is combine the two #ln# terms:

#ln(|sintheta|/|costheta|)#

Remember that #(sin)/(cos)=tan# Let's also see that, by taking the absolute values of both sin and cos, tan is forced to be positive, so we can now say:

#ln(|tantheta|)#

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How do you rewrite the expression as a single log and simplify ln|sin θ| - ln|cos θ|?

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