Question

( _______ )^2 = (csc x - 1)(csc x +1)

@terenzreignz :)

it doesn't have answer choices again!

***my answer: cot(x)

or is it tan(x) ??

is that right?

Answer 1

your answer is what now?

Answer 2

cot(x) ? :/ lol not too sure on this :/

Answer 3

Begin with the Pythagorean identity
\[\Large \cos^2(x) +\sin^2(x) = 1\]
divide everything by \(\sin^2(x)\)
\[\Large \cot^2(x) +1 = \csc^2(x)\]
bring 1 to the right side
\[\Large \cot^2(x) = \csc^2(x) - 1\]

The right side is a difference of two squares... \(x^2-y^2=(x+y)(x-y)\)

\[\Large \cot^2(x) = (\csc(x)+1)(\csc(x)-1)\]

lawl

Answer 4

oaky! :P lol :P

how do i write that tho into the blank? :/

Answer 5

cuz it's cot^2(x) right? :/

but the problem says ( ________ )^2 :/

Answer 6

cot of course :P

Answer 7

ohh and i don't need to write the "x" part? :O

Answer 8

There should already be an x there.

Answer 9

that's the thing haha... there was no x :/ it just says ( _______ )^2 = (csc x - 1)(csc x +1) :/

Answer 10

\[\left( \csc x-1 \right)\left( \csc x+1 \right)=\csc ^{2} x-1=\cot ^{2} x= \left( \cot x \right)^{2}\]

Answer 11

try cot x

Answer 12

okay, thanks you guys!! :D