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April 23rd, 2018, 03:13 AM  #1 
Newbie Joined: Apr 2018 From: East London Posts: 12 Thanks: 0  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 
April 23rd, 2018, 05:02 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
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. 
April 23rd, 2018, 05:35 AM  #3 
Newbie Joined: Apr 2018 From: East London Posts: 12 Thanks: 0 
Ok I'll see my lecturer today because that's all he gave to us ..Thank you

April 23rd, 2018, 05:43 AM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,906 Thanks: 771 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
2. is actually an identity. (Multiply both sides by sin(x)  cos(x).) I have not found a simple way to handle 3. Dan  
April 23rd, 2018, 06:56 AM  #5 
Senior Member Joined: Oct 2009 Posts: 608 Thanks: 186  
April 23rd, 2018, 07:07 AM  #6 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,906 Thanks: 771 Math Focus: Wibbly wobbly timeywimey stuff.  
April 25th, 2018, 12:59 PM  #7 
Senior Member Joined: Feb 2010 Posts: 697 Thanks: 135  $\displaystyle \dfrac{2 \sin x}{1+\cos x +(2\cos^2x1)}=\tan x$ $\displaystyle \dfrac{2\sin x}{\cos x(2\cos x+1)}=\tan x$ $\displaystyle 2\tan x = \tan x(2\cos x+1)$ $\displaystyle \tan x(2\cos x+1)2\tan x = 0$ $\displaystyle \tan x(2\cos x1)=0$. Now you can finish it. 
April 26th, 2018, 01:09 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833 
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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