Question

Can someone help me verify this?

Answer 1

1. cot x sec^4x = cot x + 2 tan x + tan^3x

Answer 2

Can you help me @mathmale ?

Answer 3

I'd love to, but I'm in the midst of helping another person with a lengthy problem. If you can find someone else who help you in this particular instance, you might get the problem done faster; otherwise, I'll help you myself when finished with the other person's issue.

Answer 4

Either way works, thanks though. :)

Answer 5

@Mertsj ? :C

Answer 6

:D

Answer 7

cot xsec^4x=cot x (sec^2 x)^2=cotx (1+tan^2 x)^2=cot x (1+2 tan^2 x+tan ^4 x)
simplify and get the R.H.S.

Answer 8

What's an RHS?

Answer 9

R.H.S.=right hand side or simply the answer you want.

Answer 10

How did you know to do that? I mean, I have a list of all of the Identities, but I would never have thought to break that 4 down to two 2's.. Just practice?

Answer 11

What did you do after the last equal sign? I understand all the way up to cot x (1+2...

Answer 12

(a+b)^2=a^2+2ab+b^2
here a=1,b=tan^2 x

Answer 13

Is that a formula I was suposed to learn?

Answer 14

yes
(a+b)*(a+b)=a*a+a*b+b*a+b*b=a^2+2ab+b^2

Answer 15

Whoa.. So how do I make both sides the same?

Answer 16

cot x(1+2 tan ^2 x+tan ^4 x)
=cot x +2 tan x *tan x*cotx+cot x*tanx*tan ^3 x
=cot x+2 tan x+tan ^3 x
( because cot x=1/tan x)

Answer 17

How do you do that in order? Like where do the parenthisis go?

Answer 18

i have multiplied each term by cot x

Answer 19

How do you know how to do that? Like cot x*2 tan^2x?

Answer 20

i know cot x=1/tan x
or cotx tan x=1

Answer 21

Okay, I think I get it a little better. I have five of these.. -__-

Answer 22

x^2=x*x
x^4=x^3*x^1=x^3*x

Answer 23

I"m reluctant to jump into your discussion at this point, because both of you (Batgirl and Surj) have already invested a lot of time there.

At this point I'll only say that it might be slightly, just slightly, easier to demonstrate that
cot x sec^4x = cot x + 2 tan x + tan^3x is "true" if we were to convert sec, csc, tan and cot to equivalent functions in sine and cosine. I won't push that idea unless asked to do so.

Answer 24

I knew we had to do that, I'm just not very good at it. I'm trying my best. :/

Answer 25

Actually we DON'T have to convert to sine and cosine functions. which would YOU rather do, continue the work you've started or convert all those cot, csc, sec and tan function to equivalents in sin and cos? Your choice.

Answer 26

Which one is easier? I know I sound lazy, but I'm behind in my class.

Answer 27

Both are rather involved, I'm sorry to say.
I've already started working on the problem arbitrarily leaving the right side alone and seeing if I can modify the left side so that it matches the right side. Does this approach make sense to you? It saves work not to modify everything; just focus on one side if possible.

Answer 28

Isn't that what we did?

Answer 29

Yes, it is. Without looking carefully at what you and surji had already done, I just summarized this approach.

Answer 30

Let me go back and review what surji has suggested; it'd be presumptuous of me to assume he's wrong. You could help me by pointing out which parts of your discussion you understand and which points raise more questions for you.

Answer 31

Aha! I just caught on fully. Wow, that took me waaaay too long. -__-

Answer 32

At first I was having issues with the full distribution, but I just got it.. I think.

Answer 33

He wrote:

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

So, are you comfortable now with this problem? Or could I still help y ou in some way?

Answer 34

At first glance I find myself in complete agreement with what he has here (immediately above.

Answer 35

How did he break down the very last part? Where it was tan^4 x cot x?

Answer 36

Working on it. Just a sec, please.

Answer 37

I'm in agreement with his result. Here's how he got it:

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Answer 38

The last term comes from (cot x)*[1 + ... + tan^4 x.
I've chosen to re-write cot x as (cos x)/(sin x) and
sin^4 x
tan^4 x as --------------
cos^4 x

and if you multiply this very last result by (cos x / sin x) the result simplifies to tan^3 x as desired.

Answer 39

Oh, gosh. That way is more confusing. But I understand. You just changed them in to their thingys...

Answer 40

Yes, I've changed cot x to cos x/ sin x and tan x to sin x / cos x.
Hope this is helpful, BG! Unfort. I'm going to have to end this conversation. If you have further questions just fire out a message and I'll respond later on. Best to you.

Answer 41

Thanks! :D