Question

Solve: cot x / tan x = csc^2 x -1
completely lost on how to solve or where to start

Answer 1

looking up ratios now

Answer 2

\[\frac{cotx}{tanx} => \frac{cosx}{sinx} * \frac{1}{tanx} => \frac{cosx}{sinx}* \frac{cosx}{sinx} => \frac{cos^2x}{sin^2x} = \frac{1}{sin^2x} -1 \]
\[ \frac{cos^2x}{sin^2x} = \frac{1-sin^2x}{sin^2x}\]
\[\frac{cos^2x}{sin^2x} - \frac{1-sin^2{x}}{sin^2x} = 0 => \]
\[\frac{cos^2x -(1-sin^2{x})}{sin^2x}=0\]

Answer 3

wouldn't I divide the sinx at the end by it self or wont it cancel?

Answer 4

what do you mean?

Answer 5

in the last part 1 - sinx^ 2/ sinx^2 wont these two cancel out because they are the same

Answer 6

I think I made a mistake somewhere; I should do it on paper lol

\[\frac{cos^2(x)}{sin^2(x)} = \frac{cos^2x}{sin^2x}\]

Answer 7

It's quite odd though.
\[\frac{cos^2(x)}{sin^2(x)} - \frac{cos^2(x)}{sin^2(x)} =0\]

Answer 8

yeah I agree

Answer 9

Hmm..i think there is something wrong with the question; we are solving for \(x\) right?
Or proving it?

Answer 10

i think solving for x but not sure.. on the sheet it just says solve.

Answer 11

can I say something? @Mimi_x3
at the first line when you got \[\frac{ 1 }{ \sin^2 x }-1= \csc^2 x -1\]. that's it

Answer 12

ok, sorry for that,. since I continue other's stuff, there is no logic there. now , i start mine

Answer 13

ok

Answer 14

what does you mean? @Loser66

Answer 15

do*

Answer 16

\[\frac{cotx}{tanx} => \frac{cosx}{sinx} * \frac{1}{tanx} => \frac{cosx}{sinx}* \frac{cosx}{sinx} => \frac{cos^2x}{sin^2x} = \frac{1-sin^2x}{sin^2x} \]
= \[\frac{ 1 }{ \sin^2x }-\frac{ \sin^2x }{ \sin^2x }= \csc^2x -1\]

Answer 17

mimi your very first line is correct. that last step is replace 1/sin^2 with csc^2 to get
csc^2 -1

Answer 18

ohh yeah..

Answer 19

I don't think you "solve" this. You prove the identity is true.

Answer 20

but the OP said "solve"

Answer 21

it is an identity

Answer 22

how can it be "solve"? since you prove 2 sides are equal. subtract to get 0 , solve for what?

Answer 23

yeah the problem stated solve but im gussesing from teachers lectures it identity because we never went over truly solving just identities so far

Answer 24

only been a few problems I have had that the outcome is either 1 or another form of identity