Verify the identity. Justify each step.

cot ( theta - pi/2) = -tan theta

@jim_thompson5910 @phi

Hint: you use these identities cot(x) = cos(x)/sin(x) cos(x+y) = cos(x)cos(y) - sin(x)sin(y) sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

@jim_thompson5910 can you show me how i am confused? i dont get what goes where?

\[\Large \cot\left(\theta - \frac{\pi}{2}\right) = -\tan(\theta)\] \[\Large \frac{\cos\left(\theta - \frac{\pi}{2}\right)}{\sin\left(\theta - \frac{\pi}{2}\right)} = -\tan(\theta)\] \[\Large \frac{\cos\left(\theta\right)\cos\left(\frac{\pi}{2}\right) + \sin\left(\theta\right)\sin\left(\frac{\pi}{2}\right)}{\sin\left(\theta\right)\cos\left(\frac{\pi}{2}\right) - \cos\left(\theta\right)\sin\left(\frac{\pi}{2}\right)} = -\tan(\theta)\] Does that help?

im still a little confused cause i dont understand where you put them, an dis that is simpliest form?

you need to show that the left side simplifies to the right side

so what you did in the last equation showed that? and it is simplified?

this is what you would do

\[\Large \cot\left(\theta - \frac{\pi}{2}\right) = -\tan(\theta)\] \[\Large \frac{\cos\left(\theta - \frac{\pi}{2}\right)}{\sin\left(\theta - \frac{\pi}{2}\right)} = -\tan(\theta)\] \[\Large \frac{\cos\left(\theta\right)\cos\left(\frac{\pi}{2}\right) + \sin\left(\theta\right)\sin\left(\frac{\pi}{2}\right)}{\sin\left(\theta\right)\cos\left(\frac{\pi}{2}\right) - \cos\left(\theta\right)\sin\left(\frac{\pi}{2}\right)} = -\tan(\theta)\] \[\Large \frac{\cos\left(\theta\right)(0) + \sin\left(\theta\right)(1)}{\sin\left(\theta\right)(0) - \cos\left(\theta\right)(1)} = -\tan(\theta)\] \[\Large \frac{0 + \sin\left(\theta\right)}{0 - \cos\left(\theta\right)} = -\tan(\theta)\] \[\Large \frac{\sin\left(\theta\right)}{-\cos\left(\theta\right)} = -\tan(\theta)\] \[\Large -\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)} = -\tan(\theta)\] \[\Large -\tan(\theta) = -\tan(\theta)\]

that verifies the identity

okay thank you !!!!!

yeah it's a lot, but just go over it again and again til it sinks in

yw

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