# Trig identity

how can i prove

tan X/sinx+cosx=sin^2 X + sinXcosX/cos X - 2cos^3X

so far i've tried using basic identities to figure it out, but i just end up getting confused.

Last edited:

The way you have written it is confusing. Are there any paranthesis missing?

assyrian_77 said:
The way you have written it is confusing. Are there any paranthesis missing?
no..

hmm lemme write it out another way

how can i prove

tanX
______
sinx+cosx

=

sin^2 X + sinXcosX
________________
cos X - 2cos^3X

CarlB
Homework Helper
Try putting x = pi/4 and see what you get.

Carl

In other words, there were parenthesis missing...

VietDao29
Homework Helper
clook said:
no..

hmm lemme write it out another way

how can i prove

tanX
______
sinx+cosx

=

sin^2 X + sinXcosX
________________
cos X - 2cos^3X
The problem is wrong. Are you sure you copied this correctly?
I think it should be:
$$\frac{\tan x}{\sin x + \cos x} = \frac{\sin ^ 2 x + \sin x \cos x}{\cos x + 2 \sin x \cos ^ 2 x}$$

VietDao29 said:
The problem is wrong. Are you sure you copied this correctly?
I think it should be:
$$\frac{\tan x}{\sin x + \cos x} = \frac{\sin ^ 2 x + \sin x \cos x}{\cos x + 2 \sin x \cos ^ 2 x}$$
i copied it as it was exactly written in the book..

arildno
Homework Helper
Gold Member
Dearly Missed
clook said:
how can i prove

tan X/sinx+cosx=sin^2 X + sinXcosX/cos X - 2cos^3X

so far i've tried using basic identities to figure it out, but i just end up getting confused.

No, you haven't copied this correctly: Put X=0
Left hand side yields 2, whereas right-hand side yields -2.

Try cancelling the common factors and try compreesing the question to its simplest form. You would then probably then get a breakthrough

arildno said:
No, you haven't copied this correctly: Put X=0
Left hand side yields 2, whereas right-hand side yields -2.

i am positive i copied it correctly. i would take a picture from the book, but i don't have a camera or scanner right now.

Hootenanny
Staff Emeritus
Gold Member
When you put x = 0 in both sides are equal to zero.

Just rewritting what clook posted in a more organised manor:

$$\frac{\tan x}{\sin x + \cos x} = \frac{\sin^2 x + \sin x \cos x}{\cos x - 2\cos^3 x}$$

Hootenanny said:
When you put x = 0 in both sides are equal to zero.

Just rewritting what clook posted in a more organised manor:

$$\frac{\tan x}{\sin x + \cos x} = \frac{\sin^2 x + \sin x \cos x}{\cos x - 2\cos^3 x}$$

This statement is equivalent to saying $$sinx=-cosx$$, so something is VERY fishy here.

-Dan

Ok clook, assuming that

$$\frac{\tan x}{\sin x + \cos x} = \frac{\sin^2 x + \sin x \cos x}{\cos x - 2\cos^3 x}$$

is what you have in your book. I worked with the RHS and got this:

$$\frac{\tan x}{\sin x-\cos x}$$

As you can see, this is different from the LHS in your equation. Something is indeed fishy here.

VietDao29
Homework Helper
clook said:
i am positive i copied it correctly. i would take a picture from the book, but i don't have a camera or scanner right now.
Okay, look at your problem again, does it say something like:
Prove this identity, or does it tell you to solve the equation?

Hootenanny
Staff Emeritus