Show that the two formulas are equivalent integral(cot(x)dx = ln|sinx| + C) and integral(cot(x)dx = -ln|csc(x)| + C) Please show steps.

Question

anonymous · Answer

Easy. So on the domain of natural log...the argument which is csc (x) has to be from (0, infinity). Therefore you can take out the absolute value sign.

anonymous · Answer

Now with the absolute value out of the way do you see how it is done

anonymous · Answer

No, not really.

anonymous · Answer

ok well csc x is 1/sin x. Therefore with log properties the constant in front of the log can be raised to the power of -1.
so therefore it becomes ln (1/csc x)=1n (sinx)
this is a proof because i left the right side of the equation unchanged

anonymous · Answer

Aha. ok, thank you! So would this one be similar: integral(cscxdx = -ln|cscx + cotx| + C)and integral(cscxdx = ln|cscx - cotx| + C )