Question

Factor and simplify :cot^4 + 2 cot^2 + 1

Answer 1

Do you know how to factor quadratics?

Answer 2

Ax^2 + Bx + c =0

Answer 3

That is the form, can you factor it into a product of binomials?

Answer 4

like (cot^4x) + 1(cot^2x) ?

Answer 5

nvm that's grouping

Answer 6

No, like x^2 +2x + 1 = (x + 1)(x+1)

Answer 7

yess

Answer 8

So, in this problem, cot^2x is like x in my factorization.

Answer 9

(cot^2 x +1)(cot^2 x +1)

Answer 10

Awesome!

Answer 11

But that can still be simplified...

Answer 12

(cot^2 x)^2

Answer 13

Don't undo all your hard work! Do you recognize cot^2x + 1?

Answer 14

yess

Answer 15

:)

Answer 16

yeah but the answers to choose from are Tan^4x
CSC^2x
sec^4x
Csc^4x

Answer 17

and that equals csc^2x

Answer 18

One of them does, but we had 2.

Answer 19

so csc^4x

Answer 20

yup

Answer 21

yayyyy

Answer 22

:)

Answer 23

These kind take practice. Keep at it!