Question

(1-tanx)^2=sec^2 x-tanx

Answer 1

I need help verifying it

Answer 2

the right hand side must be sec^2(x) -2tan(x) , re check, please

Answer 3

yes i know the answer and I have the steps I just don't understand here I'll show you what I dont understand

Answer 4

(1+tanx)^2

1-2tanx+tan^2x

(1+tan^2x)-2tanx

Answer 5

yup!! and (1+tan^2x)= sec^2 (x) and it is identity

Answer 6

yes but how did they get from that 1-2tanx+tan^2 x from (1-tanx)(1+tanx)

Answer 7

they can't !! but where does it come from? please, don't intermingle the problems.

Answer 8

*
yes but how did they get to 1-2tanx+tan^2 x from (1-tanx)(1+tanx)

Answer 9

please help me

Answer 10

I don't understand what you ask. The expression is not true
1-2tanx + tan^2 x \(\neq\) (1-tanx) (1+tanx)
but 1-2tanx + tan^2 x = (1-tanx) (1-tanx)

Answer 11

what is the question?? Is the question like " which step is false"

Answer 12

Your logic is WRONG!!

Answer 13

no the question is to verify it... I have to lists the steps and I can just go ahead and list them, but I want to understand it

Answer 14

\[(1+tanx)^2\]
\[(1-tanx)(1+tanx)\] I understand up to here
THIS STEP IS WRONG!!! you can't go from the first one to the next.
if you have \(1~~\color{red}{-}~~tan^2x\) , then it is true.
but your expression is (1+tanx)^2

Answer 15

but where did that 1 come from and how did you get the 2 up there as an exponent

Answer 16

i got confused yea I thought it went like that

(1+tanx)^2

(1-tanx)(1+tanx) but this step i assumed

so from here (1+tanx)^2 how do you move on to the next step

Answer 17

And the original one is not identity, how can you verify. This is counter example. If x = pi/4, then tanx =1 --> left hand side = (1-1)^2 =0
and the right hand side : sec (pi/4)= \(\dfrac{2}{\sqrt2}\) and \(sec^2(pi/4) = 2\)
tan (pi/4) =1 therefore the right hand side :
\[sec^2(pi/4) - tan (pi/4) = 2-1=1\]
so that the left hand side =0 \(\neq\) 1 from the right hand side
Conclusion, the expression is NOT true

Answer 18

yes it is my textbook says it is

Answer 19

can you scan your text book??

Answer 20

i screen shotted it its online

Answer 21

@UnkleRhaukus @ParthKohli @Luigi0210 someone rescues me please

Answer 22

its 13 it's highlighted pink
the first one

Answer 23

w.t ....???????????? the right hand side is \(sec^2x -\huge 2 \)tanx

Answer 24

while you post it is \(sec^2 x - tanx\)

Answer 25

yes this is the answer these are the steps, but I don't understand their processing

Answer 26

hold on let me check

Answer 27

sorry i've been doing this all day ... too many numbers

Answer 28

trash the step to the trashbin!!!
just few lines to have the process done
(1-tanx)^2 = 1 -2tanx +tan^2 x = sec^2 x -tanx
no more!!

Answer 29

trash what?

Answer 30

your post is not the good step. I don't care what they do and I don't know why you have to follow their step!! you can prove the problem by your own steps. Period

Answer 31

(1-tanx)^2 = 1 -2tanx +tan^2 x = sec^2 x -tanx .... that 1 where did you get it from? and that tan^2x ??

Answer 32

i trashed it

Answer 33

@lolabieber why do you keep posting the wrong expression?? I told you the right hand side is sec^2 x - 2 tan x, not -tan x

Answer 34

compare your post and your screenshot

Answer 35

bc you posted the wrong expression : trash the step to the trashbin!!!
just few lines to have the process done
(1-tanx)^2 = 1 -2tanx +tan^2 x = sec^2 x -tanx
no more!!

Answer 36

I trash my avatar and replace it by crying baby pic. hahahaha...

Answer 37

ok, I am sorry for it. , close the post and post it in a new one. OK?? with the screen shot

Answer 38

yes i Know the -2tanx but can you please tell me what you thought in order to put that 1 -2tanx +tan^2 x ... sorry I'm making you cry imagine me :(

Answer 39

this post im new here too hah?

Answer 40

close it.

Answer 41

in the top right, you see the box "Close" click it

Answer 42

post another new

Answer 43

i did and i closed it but it opened again