Question

(_____)^2 = (csc x-1)(csc x+1)
What is suppose to be in the blank?
***I know this is a trig identity and do not have my sheet with me. No online refrences are helping me***

Answer 1

I know it has to be either tan x or cot x. My memory is not on my side today.

Answer 2

ok.. there are three trig identities.
the most common is
\[\cos^2x+\sin^2x=1\]

Answer 3

but there are two more equations.

Answer 4

Ok

Answer 5

\[1+\tan^2x=\sec^2x\]
\[1+\cot^2x = \csc^2x \]

Answer 6

let's solve the right hand side of the equation to see who is the culprit lol xD so we expand \[(cscx-1)(cscx+1)\]

Answer 7

Haha ok

Answer 8

just use foil ... you will notice that O and I cancel out

Answer 9

Not familiar with FOIL (Sorry). My teacher calls it the "F word" (lol)

Answer 10

first outer inner last

Answer 11

\[(cscx-1)(cscx+1) = (cscx)(cscx)+(1)(cscx)+(-1)(cscx)+(1)(1)\]

Answer 12

fffffffff missed a sign on the last one should be +(-1)(1)

Answer 13

Oh ok! I think I see what you are getting at

Answer 14

\[(cscx-1)(cscx+1) = (cscx)(cscx)+(1)(cscx)+(-1)(cscx)+(-1)(1) = (cscx)^2+cscx-cscx-1\]

Answer 15

OY ! \[(cscx)^2+cscx-cscx-1 \]

Answer 16

the cscx-cscx cancels out

Answer 17

\[\csc^2x-1\]

Answer 18

Then we can add the 1 right?

Answer 19

do you remember \[1+\cot^2x = \csc^2x ? \]

Answer 20

what do I need to do have \[\cot^2x \] by itself

Answer 21

Yep!

Answer 22

subract the 1?

Answer 23

yes subtract on both sides..

Answer 24

Oh ok! So we just proved that cot^2 (x) is my answer right?

Answer 25

yeah

Answer 26

\[\cot^2x = \csc^2x-1\]

Answer 27

Would I just write it as cotx?

Answer 28

huh? you mean for
(cotx)^2 = (csc^2x-1)

Answer 29

Yes

Answer 30

hmmm... if you don't forget this part
\[\cot^2x = \csc^2x-1 \]

Answer 31

\[(cotx)^2 = (cscx)^2-1\]
means the same

Answer 32

just don't write cot2x and csc2x-1
BIG NO NO!

Answer 33

Ok! Thank you for your time and teaching me!

Answer 34

if u observe the RHS, u see it results csc^2-1
there is also an identity saying that,
cosec^2-cot^2=1
that implies cosec^2-1=cot^2...therefore theRHS is cot^2
therefore obviously LHS must be cot^2...therefore the answer is cot

Answer 35

^ done already lol

Answer 36

the term cosecant isn't used for the Pythagorean identities.

Answer 37

but there is one identity that is used beyond trig and that's the \[\cos^2x+\sin^2x = 1 \]