Question

Verify the identity. cot((x - (pi/2)) = -tan x

Answer 1

well cot (90-x)=tanx
that should help ya

Answer 2

I always thought that it is an identity like this (?)

Answer 3

um..can you give me some more details..? i'm a bit confused...

Answer 4

im not sure but u've got x-90 so that should give a -tan x as i showed u the formula before

Answer 5

\(\normalsize\color{black}{\rm{hint}~~~~~~~~\tan(-a)=-\tan(a)}\)

Answer 6

yea that one

Answer 7

There are identities for sin (a+b), sin (a-b), cos (a+b), and so on, and similarly, there are identities for tan (a+b) and tan (a-b). Have you a table of trig identities? You need the one for tan (a-b). cot (a-b) would be the reciprocal of that.

Answer 8

tan (A-B) = (tanA-tanB)/1+tanAtanB

Answer 9

so substitute A with x and B with 90

Answer 10

is that right^ @SolomonZelman

Answer 11

oh my bad flip it for cotangent

Answer 12

The thing here is just

\(\normalsize\color{black}{ \cot((x - (pi/2)) = -\tan x}\)
\(\normalsize\color{black}{ \cot(x -90) = -\tan x}\)
\(\normalsize\color{black}{ \cot(~~-~[90 -x]~~) = -\tan x}\)
\(\normalsize\color{black}{ -\cot(~~[90 -x]~~) = -\tan x}\)
\(\normalsize\color{black}{ \cot(~~90 -x~~) = \tan x}\)

Answer 13

so... so far, using the reciprocal identity(theorem..? whatever) it's gonna be like:
cot(x-(π/2)) = -tanx
cot(x-(π/2)) = tan(-a)
tan(1/(x-(π/2)) = tan(-a)
so (1/(x-(π/2)) = -a?

Answer 14

I got what I got, don't know about others

Answer 15

cot (x-90)=(1+tanxtan90)/(tanx-tanB)
= (1+undefined)/tanx - undefined)
Oops

Answer 16

@alissatim found that someone asked this question on open study too
http://openstudy.com/study#/updates/50a94805e4b082f0b8534faa

Answer 17

well, only if you consider \(\normalsize\color{black}{ \cot(90 -x) = \tan x}\) to be an identity. Because on some level, even `sin²x+cos²x=1` has to be proven.

Answer 18

study, it okay we answered I think :)

Answer 19

oops, my bad, it's invalid. :)

Answer 20

what's invalid ?

Answer 21

thank you so much!! :) @study100

Answer 22

oh also, when the question says to verify the identity, does it want me to have the name of the certain identity? i mean.. like do i have to name it?

Answer 23

it wants you to show that both sides are equal to each other.

Answer 24

Using only 1 side of the problem

Answer 25

Just fyi, it's a confunction identity.

Answer 26

In general,

"verify the identity" - manipulate 1 side only
"prove the indentity" - manipulate both sides as much as you feel like

Answer 27

I go this way:
\[cot (x-\pi/2)=\dfrac{cos(x-\pi/2)}{sin(x-\pi/2)}=\dfrac{cosxcos\pi/2+sinxxin\pi/2}{sinxcos\pi/2-cosxsin\pi/2}=-\dfrac{sinx}{cosx}= -tanx\]

Answer 28

you forgot to close the question