Question

Proving Identities:
csc^4x-csc^2x = cot^4x+cot^2x ?
How ?

Answer 1

So let's manipulate the left side and make it match the right side.
We'll need to recall one of our Square Identities:\[\large 1+\cot^2x=\csc^2x\]We'll rewrite the left side in terms of cotangents.

Answer 2

ok.

Answer 3

\[\large \csc^4x-\csc^2x \qquad= \qquad (\color{green}{\csc^2x})^2-\color{green}{\csc^2x}\]From here we'll apply our identity,\[\large =(\color{green}{1+\cot^2x})^2-\color{green}{1+\cot^2x}\]

Answer 4

hmmm

Answer 5

Woops I should have put brackets around the second identity.
We need to distribute that negative sign. That was sloppy of me :)\[\large =(\color{green}{1+\cot^2x})^2-\color{green}{(1+\cot^2x)}\]

Answer 6

ahahah. that's ok.

Answer 7

Which part you confused on? The way I split up the 4th power giving you trouble? :o

Answer 8

I'm analyzing it sir. but I get it. :)

Answer 9

If you expand out that first set of brackets, you'll see some nice cancellations afterward.
Try itttttt! :U

Answer 10

:) ok sir.

Answer 11

thanks sir I get it now.

Answer 12

cool c:

Answer 13

:)