Question

how do a verify the expression sec^2 = 2tanx + 2tan^3x

Answer 1

\[\sec^2x=2tanx+2\tan^2x\]
definition,
Sec^2x=Tan^2x+1
\[Tan^2x+1=2tanx+2\tan^3x\]

Do it.

Answer 2

proving or solving that equation ?

Answer 3

Do you have to use one side independently?

Answer 4

I'll assume no, OK?

Answer 5

\[Tan^2x+1=2Tanx+2Tan^3x\]

Answer 6

this is it, sorry again.

Answer 7

\[Tan^2x+1=2Tanx(Tan^2+1)\]

2tanx has to be equal one.

this is not an identity, it's an equation to solve

Answer 8

\[x= Tan ^{-1}(1/2)\]

Answer 9

Did I go too fast?

Answer 10

Can someone help me with my literature question?
http://openstudy.com/study#/updates/529a99bfe4b0a454724fff80

Answer 11

\[Sec^2x=Tan^2x+1~~~~~~~~~~So,\]\[Tan^2x+1=2Tanx+2Tan^3x\]\[Tan^2x+1=2Tanx~(1+Tan^2x)~~~~~~can cel~~out~~(Tan^2x+1)\]\[2Tanx=1~~~~~~->~~~~~~~~~~~~Tan ^{-1}(1/2)\]

Answer 12

that's it basically.
Again, this is NOT an IDENTITY!

Answer 13

the degrees of LHS is 2 while RHS is 3, obviously this cant be an identity :)

Answer 14

This is a rate of change problem so I'm not sure if I have to prove it or solve it. The problem says to verify that the trigonometric expression for the rate of change is also 2 tanx + 2 tan^3x. the most confusing part about this problem is that I can't tell whether it's an identity or not.

Answer 15

Right, it's not an identity, did you look at my work? I showed that it's not an identity.
You can also check by plugging in values for x.

Answer 16

Look,
let's take 90.
x=90

and Tan=Sin/Cos

we can plug this into \[Tan^2x+1=2Tanx+2Tan^3x\]
this is undefined b/c Co90=0

Do you understand this?