Question

Cot x Sec^4 x = Cot x + 2tan x + tan^3 x

Answer 1

Is this an identity to be proven?

Answer 2

yes

Answer 3

Does your teacher care which side you work on?

Answer 4

They said to have me match the right side with the left, but I don't think it matters.

Answer 5

have you tried anything yet?

Answer 6

I was thinking I might be able to factor it.

Answer 7

to me, I replace sec^4 x = (1 = tan^2)^2 and then expand it, and then time cot , and get the RHS

Answer 8

1+tan^2 not 1=tan^2 sorry

Answer 9

thank you so much! that helps!

Answer 10

yw

Answer 11

i don't actually see how that works out. i get an extra 1 and the cotx is still multiplying by what is inside the factored out equation.

Answer 12

\[\cot x(1+\tan ^2x)^2=\cot x(1+2\tan ^2x+\tan ^4x)=\cot x \cot +2\cot x \tan ^2x+\cot x \tan ^4x\]

Answer 13

Hang on...I'll fix that

Answer 14

\[\cot x+2\cot x \tan ^2x+\cot x \tan ^4x\]

Answer 15

Do you agree so far?

Answer 16

Hoa...any mistakes there?

Answer 17

yes

Answer 18

So we have the cotx. Let's see if we can show that the other two terms are equal to the two terms on the right.

Answer 19

\[2\cot x \tan ^2x=2\cot x \tan x \tan x=2\tan x\]

Answer 20

Do you see that?

Answer 21

Now you do the same thing to the last term

Answer 22

And you will be done.

Answer 23

thank you! I will do that!

Answer 24

you're welcome and thanks to Hoa as well

Answer 25

thank you both!