cot x sec^4x = cot x + 2 tan x + tan^3x
this is the problem I need to simplify. I'm not certain whether I can think of something like 2 tan as tan^2. I'm also having problems finding identities that will help me. Thank you so much!

Question

anonymous · Answer

What happens when you sub $\sec^2(x) = \tan^2(x)+1$?

anonymous · Answer

Since $\sec^4(x) = [\sec^2(x)]^2$

anonymous · Answer

So i can use that formula, but instead of tan^2(x) + 1. I do [tan^2(x) + 1]^2?

anonymous · Answer

Exactly

anonymous · Answer

Then foil it out and see if you've gotten closer.

anonymous · Answer

cot x  [tan^2(x) + 1]^2 = cot x + 2 tan x + tan^3x which turns into : 
 cot x tan^4(x^2) + 1 = cot x + 2 tan x + tan^3x

correct?

anonymous · Answer

Not quite...
$$
[\tan^2(x)+1]^2 = [\tan^4(x) + 2\tan^2(x) + 1] 
$$

anonymous · Answer

Since $\cot(x) = 1/\tan(x)$ it will basically lower the power of the $\tan(x)$ terms.

anonymous · Answer

Sorry, I'm not sure where you got the 2 tan ^2 from