Question

Verify the identity.

tan x plus pi divided by two = -cot x

Answer 1

Well? Do you know how to verify things?
What does an Identity mean? If you know, then test for it, see if it holds up.

Answer 2

i do not. that is why i am at open study. it is an opened question and just needs to be worked out. its a free response. i have about 5 minutes to finish this problem before he thing logs me out. so any help would be apprecitsated

Answer 3

sorry you're in a hurry. Unfortunately, your "tan x plus pi divided by two = -cot x" is open to misinterpretation. Do you mean \[\tan x + \pi .or. \tan(x+\pi)?\]Parentheses make a huge difference.

Answer 4

Assuming that you mean\[\frac{ \tan(x+\pi) }{ 2 }\]=-cot x

Answer 5

\[\tan(x+\frac{\pi}{2})\]

Answer 6

looks like \[\tan (x + \frac{\pi}{2})=-\cot( x )\]

Answer 7

...look for the "sum formula for the tangent function."

Answer 8

@Nnesha got it

Answer 9

You see, there seem to be no fewer than 3 interpretations of your stated problem because of the lack of parentheses.
You may not like this nitpicking, but in the long run it will save you much time and frustration.

Answer 10

Might be better were you to DRAW your equation in the Draw utility, below. Could you do that, please?

Answer 11

@mathmale i dont mind it at all and completely understand. @Nnesha has the correct problem

Answer 12

there are different ways to verify the identity
are you familiar with Negative Angle Identities , Cofunctions Identities ?
what's the reciprocal of tan ?

Answer 13

it is obvious which one it is since the others wont work.

Answer 14

I stand by my suggestion to use parentheses wherever there may be any ambiguity, or to draw the problem statement, or to use Equation Editor.

Answer 15

Even if it may be obvious in this problem, getting into the habit of putting parenthesis is never bad. It helps everyone so that nobody misinterprets anything, and the user also benefits from it.

Answer 16

Clearer formatting translates into less errors too

Answer 17

@Nnesha problem does not give any specific way but im guessing the most basic will be the best. @LanHikari22 i will use parenthesis next time

Answer 18

I like cofunctions ^^ as Nnesha mentioned.
Seems like a good approach.

Answer 19

@jon321 I wonder if by verification, you only mean that they are equal, because then you can verify by simply putting any x in both sides and see if both sides of the equation are equal, since verification could be different from proving.

Answer 20

wait i think there is a negative sign

Answer 21

\[\sin\left(x+\frac{\pi}{2}\right)=\cos(x)\]

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

Answer 22

I want to present it in a slightly intuitie sense, so perhaps you may want to check this:
https://www.desmos.com/calculator/ndhdgnqqpa

Answer 23

You may move a and b to shift both functions by multiples of approximately \[\pi/2\]
The functions look like circles because they are in polar form, but it is still the same function. I just think it's intuitive to see the circles shifting in this sense.

Answer 24

Perhaps this diagram might illustrate the shifting more. Please correct me if I'm wrong anywhere.