Another one about verifying the identity! Please help

Question

anonymous · Answer

attachment

anonymous · Answer

@dtuniyants you were very helpful, I'd appreciate it if you could help me with one more!

anonymous · Answer

of course, just a sec, I nedd to solve it

anonymous · Answer

When simplified it looks like this:
$$1/(\tan(x-\pi/2))=-\tan(x)$$

anonymous · Answer

the absolute values of -tan(x) and tan(x-pi/2) have to be equal 1.

anonymous · Answer

How did you go about changing cot to tan? :/

anonymous · Answer

|tan(x)| can only be equal 1, when x=pi/4, 3pi/4, 5pi/4, and 7pi/4. All of these can be answers to the equation. Since there are no restrictions in range of function cot(x), all of these can be answers

anonymous · Answer

cot=1/tanx

anonymous · Answer

|dw:1417638260413:dw|
Since every quadrant the sign of tan(x) changes they all are answers to the equation