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April 23rd, 2018, 02:13 AM   #1
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Red face Determine the values of the variables for which each of the following identities

1.{2x / Cosx- Sinx} = Cosx + Sinx

2.{1 - Sin 2x}/ {Sinx- Cosx} = Sinx - Cosx

3.{Sinx + Sinx} /{1 + Cosx + Cos2x} = Tanx


Determine the values of the variables for which each of the following identities are undefined......

Please help i just need get through matric
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April 23rd, 2018, 04:02 AM   #2
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I'm afraid that doesn't quite make sense. First, an "identity" is an equation that is true for all values of x and so must be defined for all values of x. What you have are not identities but equations. But the word "equation" doesn't make sense here either because it is an "expression", perhaps the left of right side of an equation, that is or is not defined. Finally, I don't know what "matric" means. I thought perhaps "matrix" or "metric" but neither of those has anything to do with this problem.

Sine and Cosine themselves are defined for all x. Tan(x) is undefined for x equal to odd multiples of $\displaystyle \frac{\pi}{2}$. Fractions are undefined when the denominator is undefined.
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April 23rd, 2018, 04:35 AM   #3
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Ok I'll see my lecturer today because that's all he gave to us ..Thank you
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April 23rd, 2018, 04:43 AM   #4
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Quote:
Originally Posted by Vee88 View Post
1.{2x / Cosx- Sinx} = Cosx + Sinx

2.{1 - Sin 2x}/ {Sinx- Cosx} = Sinx - Cosx

3.{Sinx + Sinx} /{1 + Cosx + Cos2x} = Tanx


Determine the values of the variables for which each of the following identities are undefined......

Please help i just need get through matric
1. can only be solved numerically.

2. is actually an identity. (Multiply both sides by sin(x) - cos(x).)

I have not found a simple way to handle 3.

-Dan
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April 23rd, 2018, 05:56 AM   #5
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2. is actually an identity. (Multiply both sides by sin(x) - cos(x).)
It is not though. It doesn't hold for $x=\pi/4$.
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April 23rd, 2018, 06:07 AM   #6
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It is not though. It doesn't hold for $x=\pi/4$.
Well, okay, except for values that aren't allowed in the original expression.

Thanks for the catch.

-Dan
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April 25th, 2018, 11:59 AM   #7
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3.{Sinx + Sinx} /{1 + Cosx + Cos2x} = Tanx
$\displaystyle \dfrac{2 \sin x}{1+\cos x +(2\cos^2x-1)}=\tan x$

$\displaystyle \dfrac{2\sin x}{\cos x(2\cos x+1)}=\tan x$

$\displaystyle 2\tan x = \tan x(2\cos x+1)$

$\displaystyle \tan x(2\cos x+1)-2\tan x = 0$

$\displaystyle \tan x(2\cos x-1)=0$. Now you can finish it.
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April 26th, 2018, 12:09 AM   #8
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Was the first equation intended to be $\displaystyle \frac{\cos 2x}{\cos x - \sin x} = \cos x + \sin x$?

That holds except when $ x = \pi/4 + \text{k}\pi$, where k is an integer.
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