Question

Verify the identity. Justify each step.

Answer 1

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

Answer 2

@jim_thompson5910 @phi

Answer 3

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)

Answer 4

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

Answer 5

\[\Large \cot\left(\theta - \frac{\pi}{2}\right) = -\tan(\theta)\]


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


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


Does that help?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

this is what you would do

Answer 10

\[\Large \cot\left(\theta - \frac{\pi}{2}\right) = -\tan(\theta)\]



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



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



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



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



\[\Large \frac{\sin\left(\theta\right)}{-\cos\left(\theta\right)} = -\tan(\theta)\]



\[\Large -\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)} = -\tan(\theta)\]



\[\Large -\tan(\theta) = -\tan(\theta)\]

Answer 11

that verifies the identity

Answer 12

okay thank you !!!!!

Answer 13

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

Answer 14

yw