Verify that the equation is an identity. Show that ln|cosa|- ln|cota|= ln|sina|. Please show all steps.

Answer 1

Subtraction of logs is the same as dividing the numbers inside the log so:

ln|cos(a)| - ln|cot(a)| is the same as ln|cos(a)/cot(a)| and since cot(a) = cos(a)/sin(a) we can say ln|cos(a)| - ln|cot(a)| is the same as ln|cos(a)/(cos(a)/sin(a)|

Then, simplifying what's inside: