Question

Simplify cot x sec^4x = cot x + 2 tan x + tan^3x

I've kept hitting dead ends. Could someone help? Just to start out.

Answer 1

start by multiplying the left and right sides by tan(x), and remember that (tanx)*(cotx)=1... is that enough for you to get it?

Answer 2

So it'd start out as sec^4x = 1 +2tan^2x + tan^4x?

Answer 3

right. Do you see where to go from there?

Answer 4

Yes I do. Thank you very much!

Answer 5

you're welcome

Answer 6

tan x(cot x sec^4x) = tan x(cot x) + (tan x)2 tan x + tan^3x(tan x)
sec^4x = 1 + 2 tan^2x + tan^4x
sec^4x = (tan^2x + 1)^2
sec^2x = tan^2x + 1
sec^2x = sec^2x

Like so?

Answer 7

yep!