Simplifying an Expression: ln|cscu – cotu| + c

ln|cscu-cotu|+c

We are given the expression: ln|cscu-cotu| + c

To start, let’s simplify the absolute value notation

We are given the expression: ln|cscu-cotu| + c

To start, let’s simplify the absolute value notation. Recall that the absolute value of a number is always positive. Therefore, we can remove the absolute value and consider two cases: cscu – cotu > 0 and cscu – cotu < 0. Case 1: cscu - cotu > 0
In this case, we can rewrite the expression as ln(cscu – cotu) + c.

Case 2: cscu – cotu < 0 In this case, cscu is less than cotu, which means u is in the third or fourth quadrant of the unit circle. In these quadrants, cscu is negative and cotu is positive. So, the expression becomes ln(-cscu + cotu) + c. Now, let's discuss each of these cases individually. Case 1: cscu - cotu > 0
In this case, we have ln(cscu – cotu) + c.
The logarithm function ln(x) gives the natural logarithm of x.G1234

Therefore, the expression simplifies to:
ln(cscu – cotu) + c

Case 2: cscu – cotu < 0 In this case, we have ln(-cscu + cotu) + c. The logarithm of a negative value is not defined in the real number system. Hence, for this case, the expression is undefined. In summary, the simplified expression depends on the value of cscu - cotu. If cscu - cotu > 0, the expression simplifies to ln(cscu – cotu) + c.
If cscu – cotu < 0, the expression is undefined.

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