C3 - trig

Hello, I'm stuck/confused with the following.

Tan^2X+2tanx+1 express in terms of cotx. I think it's (cot^2x)+(1/2cotx)+1. But there's a devil in me trying to make believe its (cot^2x)+(2cotx)+1 - surely this can't be right? Which one is it :angry:

Reply 1

TeeEm

19

Original post by Cool-Light

Hello, I'm stuck/confused with the following.

Tan^2X+2tanx+1 express in terms of cotx. I think it's (cot^2x)+(1/2cotx)+1. But there's a devil in me trying to make believe its (cot^2x)+(2cotx)+1 - surely this can't be right? Which one is it :angry:

I do not follow your argument
would you be as kind as to post your working?

Reply 2

Actaeon

11

Original post by Cool-Light

Hello, I'm stuck/confused with the following.

Tan^2X+2tanx+1 express in terms of cotx. I think it's (cot^2x)+(1/2cotx)+1. But there's a devil in me trying to make believe its (cot^2x)+(2cotx)+1 - surely this can't be right? Which one is it :angry:

2tanx is simply (2)x(tanx). You can then change (tanx) to (1/cotx) so you end up with (2)x(1/cotx) which is (2/cotx). I think :smile:

(the 'x's outside the brackets being multiplication signs rather than the variable x)

(edited 9 years ago)

Reply 3

username1560589

20

Original post by Cool-Light

Hello, I'm stuck/confused with the following.

Tan^2X+2tanx+1 express in terms of cotx. I think it's (cot^2x)+(1/2cotx)+1. But there's a devil in me trying to make believe its (cot^2x)+(2cotx)+1 - surely this can't be right? Which one is it :angry:

\tan x = \frac{1}{\cot x}

\therefore \tan^{2} x + 2\tan x + 1 = \cot^{-2} x + 2 \cot^{-1} x + 1

Reply 4

Cool-Light

OP

2

Original post by TeeEm

I do not follow your argument
would you be as kind as to post your working?

Ahhh, here's the original question manipulated by me. "Simplify the following expressions to a single term"

Question: (tan^4x)+(2tan^x)+1, please don't solve it, it's one of my homework questions, I just need a hint. So I tried that up there in order to experiment and see where I get...

Reply 5

Cool-Light

OP

2

Original post by morgan8002

\tan x = \frac{1}{\cot x}

\therefore \tan^{2} x + 2\tan x + 1 = \cot^{-2} x + 2 \cot^{-1} x + 1

Oh, so the devil turned out to be angel :smile:

. Thank you for clearing the misconception

Reply 6

TeeEm

19

Original post by Cool-Light

Ahhh, here's the original question manipulated by me. "Simplify the following expressions to a single term"

Question: (tan^4x)+(2tan^x)+1, please don't solve it, it's one of my homework questions, I just need a hint. So I tried that up there in order to experiment and see where I get...

look at post 4
is what morgan8002 has written your question because what you have typed is ambiguous

OP

Wait what...?

OP

Original post by TeeEm

look at post 4
is what morgan8002 has written your question because what you have typed is ambiguous

So there's more than one way of writing it?

Reply 9

username1560589

20

Original post by Cool-Light

Ahhh, here's the original question manipulated by me. "Simplify the following expressions to a single term"

Question: (tan^4x)+(2tan^x)+1, please don't solve it, it's one of my homework questions, I just need a hint. So I tried that up there in order to experiment and see where I get...