Find All Solutions of the Equation Tanxsecx 2tanx

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Precalculus Mathematics Homework Help

Trig identity problem: ((sec x - tan x)^2 +1)/(sec x cscx) - (tanx secx ) = 2 tan x

Thread starter Hsopitalist
Start date Mar 11, 2020

Homework Statement:: ((sec x - tan x)^2 +1)/(sec x cscx) - (tanx secx ) = 2 tan x

Relevant Equations:: multiple trig identities

This is my first attempt to ask for help on here. I'm not in school (52 years old) but just exploring. This is a problem from an old Lial text from 2001.

I have worked on this problem for almost an hour now and just need some resolution. I have four pages of notes here. I have tried all kinds of substitutions and can't get a way to connect the two sides. It's number 48 on page 200 for those who have it. Can someone give me a clue for how to solve this?
Thanks.

Answers and Replies

Homework Statement:: ((sec x - tan x)^2 +1)/(sec x cscx) - (tanx secx ) = 2 tan x

@Hsopitalist, just to be clear, is the identity you're trying to prove this (which is what you wrote):
$$\frac{(\sec x - \tan x)^2 + 1}{\sec x\csc x} - \tan x\sec x = 2\tan x$$
or is it this one?
$$\frac{(\sec x - \tan x)^2 + 1}{\sec x\csc x - \tan x\sec x} = 2\tan x$$
Edit : Both equations are edited to correctly reflect the original equation.
We've had a lot of members who wrote something like x^2 - 1/x - 1, when what they meant was (x^2 - 1)/(x - 1).
An expression written as x^2 - 1/x - 1 would usually be interpreted to mean ##x^2 - \frac 1 x - 1##.

Last edited: Mar 17, 2020

Mark44

Interesting, thanks for that observation. I guess I should've put another set of parenthesis around the entire denominator. Which brings me to how were you able to write what you wrote? I like that way better than the method I used.

Sean

I gather it was this one:
$$\frac{(\sec x - \tan x)^2 + 1}{\sec x\csc x - \tan x\sec x} = 2\tan x$$

Here's the TeX script I wrote, $$\frac{(\sec x - \tan x)^2 + 1}{\sec x\csc x - \tan x\sec x} = 2\tan x$$

We have a LaTeX guide -- a link to it appears in the lower left corner.

Last edited: Mar 17, 2020

$$\frac{(\sec x - \tan x)^2 + 1}{\sec x\csc x - \tan x\sec x} = 2\tan x$$

Oh how cool is that. Thanks!

Last edited by a moderator: Mar 17, 2020

While I'm at it, I know there are programs like MATLAB and Mathematica. Is it worthwhile to start learning one of those or just save it until it comes up in a pedagogical format?

how so?

Archaic

Thanks for your input, this is why I love this website! My comment "how cool is that" was in reference to the fact that I had never used LaTeX before, not the equation itself.

The correct equation was in my original post, in the denominator there should have been "- tanx secx" whereas as I originally wrote it it seemed to be a term onto itself and not under the denominator.

Both are wrong; just checked with desmos. You can also take ##x=\frac{\pi}{4}##.

I miscopied two of the trig functions in the posted identity. I've gone back an edited my post to correct the equations.

As it turns out, this expression is not an identity.

##\displaystyle \frac{(\sec x - \tan x)^2 + 1}{\sec x\csc x - \tan x\sec x} = 2\tan x ##

Modify it by replacing the last sec(x) with csc(x). The result is a trig identity.

##\displaystyle \frac{(\sec x - \tan x)^2 + 1}{\sec x\csc x - \tan x\csc x} = 2\tan x ##

Last edited: Mar 17, 2020

Chaffey Thounater44

Find All Solutions of the Equation Tanxsecx 2tanx

Trig identity problem: ((sec x - tan x)^2 +1)/(sec x cscx) - (tanx secx ) = 2 tan x

Answers and Replies

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