Trig Identities: csc^4(x)-2csc^2(x)+1=cot^4(x)

[kwal]

Hi, I have a question from my homework sheet. This one problem is stumping me and I'm a bit confused:
csc^4(x)-2csc^2(x)+1=cot^4(x)

So far I have:
(1/sin^4(x))-(1/2sin^2(x))+1=cos^4(x)/sin^4(x)

If anyone could help me verify the identity that would be great. I tried looking at it on Mathway, because I have a subscription, but there aren't any steps available.

 

[Deleted member 4993]

Hi, I have a question from my homework sheet. This one problem is stumping me and I'm a bit confused:
csc^4(x)-2csc^2(x)+1=cot^4(x)

So far I have:
(1/sin^4(x))-(1/2sin^2(x))+1=cos^4(x)/sin^4(x)

If anyone could help me verify the identity that would be great. I tried looking at it on Mathway, because I have a subscription, but there aren't any steps available.

Start simplyfying the left-hand-side of the given identity - using csc²(x) = 1 + cot²(x):

csc^4(x)-2csc^2(x)+1

= [1 + cot²(x)]² - 2*[1 + cot²(x)] + 1

and continue....

 

[pka]

Hi, I have a question from my homework sheet. This one problem is stumping me and I'm a bit confused: csc^4(x)-2csc^2(x)+1=cot^4(x)

I would note that $\displaystyle \csc^4(x)-2\csc^2(x)+1=(\csc^2(x)-1)^2$

 

[kwal]

Is this correct?

 

[Deleted member 4993]

Is this correct?

Almost!!

You are missing "x" in the LHS of the second line.