Question

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

Answer 1

change cot to sin and cos

Answer 2

@jonask how do you do hat ? I need help with this

Answer 3

\[\cot \theta=\frac{ \cos \theta }{ \sin \theta }\]
use the theta above x-pi/2

Answer 4

So cot theta = x-pi/2?

Answer 5

no cot theta=cot (x-pi/2)

Answer 6

now what ?

Answer 7

use the identity above that writes cot as cos /sin

Answer 8

I thought the result would be cot theta = -tanx

Answer 9

lets use this id first\[\cot(x-\pi/2)=\frac{\cos (x-\pi/2)}{\sin (x-\pi/2)}\]

Answer 10

-tanx= cot(x-pi/2)

Answer 11

right ? im not sure of the steps

Answer 12

@jonask

Answer 13

we are proving it here so according to the last step we simplify as\[\frac{ -\sin x }{ \cos x }=-\tan x\]
this equal to -tan x

Answer 14

So what do I do for the steps i need help working it out ... @jonask

Answer 15

\[\cot (x-\pi/2)=\frac{ \cos (x-\pi/2) }{ \sin(x-\pi/2) }=\frac{ \cos(\pi/2-x )}{ -\sin(\pi/2-x) }=\frac{ \sin x }{ -\cos x }=-\tan x\]

Answer 16

THANK YOU SO MUCH !!!! @Jonask